The list of the first , 8, moments is (where Hn[i] is the partial sum of Zeta(i)) 2 [-4 n + Hn[1] (2 n + 2), n (7 n + 13) + Hn[1] (-2 n - 2) - 4 (n + 1) Hn[2], 2 2 -n (19 n + 81 n + 104) + Hn[1] (14 n + 14) + 12 (n + 1) Hn[2] 3 2 3 n (2260 n + 9658 n + 15497 n + 11357) + 16 (n + 1) Hn[3], --------------------------------------- 9 2 2 2 - 2 (n + 1) (42 n + 78 n + 77) Hn[1] + 12 (n + 1) Hn[1] 2 2 3 + (-4 (42 n + 78 n + 31) (n + 1) + 48 (n + 1) Hn[1]) Hn[2] 4 2 3 4 + 48 (n + 1) Hn[2] - 96 (n + 1) Hn[3] - 96 (n + 1) Hn[4], 4 3 2 n (229621 n + 1422035 n + 3401325 n + 3915865 n + 2217794) - ------------------------------------------------------------- 108 3 2 2 2 + 2 (n + 1) (190 n + 1300 n + 1950 n + 1171) Hn[1] - 280 (n + 1) Hn[1] 3 2 2 3 + (20 (38 n + 204 n + 286 n + 91) (n + 1) - 800 (n + 1) Hn[1]) Hn[2] 4 2 - 480 (n + 1) Hn[2] + 2 3 4 5 (80 (14 n + 26 n + 17) (n + 1) - 320 (n + 1) Hn[1] - 640 (n + 1) Hn[2]) 4 5 5 Hn[3] + 960 (n + 1) Hn[4] + 768 (n + 1) Hn[5], n (74250517 n 4 3 2 + 523547007 n + 1579578725 n + 2571768745 n + 2342670258 n + 1133389148 )/2700 4 3 2 - 2/3 (n + 1) (11300 n + 56270 n + 135760 n + 145510 n + 68427) Hn[1] / 2 2 2 3 3 | + 20 (63 n + 117 n + 329) (n + 1) Hn[1] - 120 (n + 1) Hn[1] + | \ 4 3 2 2 4 (11300 n + 51710 n + 101830 n + 93640 n + 26013) (n + 1) - -------------------------------------------------------------- 3 \ 2 3 4 2| + 240 (21 n + 39 n + 68) (n + 1) Hn[1] - 720 (n + 1) Hn[1] | Hn[2] / 2 4 5 2 + (240 (21 n + 39 n + 37) (n + 1) - 1440 (n + 1) Hn[1]) Hn[2] 6 3 3 2 3 - 960 (n + 1) Hn[2] + (-160 (38 n + 225 n + 325 n + 159) (n + 1) 4 5 6 2 + 7360 (n + 1) Hn[1] + 9600 (n + 1) Hn[2]) Hn[3] + 2560 (n + 1) Hn[3] 2 4 5 + (-480 (21 n + 39 n + 37) (n + 1) + 2880 (n + 1) Hn[1] 6 5 6 + 5760 (n + 1) Hn[2]) Hn[4] - 11520 (n + 1) Hn[5] - 7680 (n + 1) Hn[6], 6 5 4 3 - 7 n (4361821529 n + 36987323153 n + 135379990924 n + 280732243290 n 2 + 356835588161 n + 275702876557 n + 119672624386)/81000 + 1/18 (n + 1) ( 5 4 3 2 1607347 n + 12169045 n + 35117495 n + 56653667 n + 48253086 n 3 2 2 2 + 19517436) Hn[1] - 28 (285 n + 2685 n + 4290 n + 6208) (n + 1) Hn[1] 3 3 + 5880 (n + 1) Hn[1] + (7 5 4 3 2 (229621 n + 1557635 n + 4086825 n + 5641645 n + 4118354 n + 1044612) 2 3 2 3 (n + 1) /9 - 112 (285 n + 2265 n + 3510 n + 3559) (n + 1) Hn[1] 4 2 + 28560 (n + 1) Hn[1] ) Hn[2] + 3 2 4 5 (-1680 (19 n + 123 n + 182 n + 122) (n + 1) + 43680 (n + 1) Hn[1]) / 2 6 3 | Hn[2] + 20160 (n + 1) Hn[2] + | \ 4 3 2 3 112 (11300 n + 53420 n + 115420 n + 114700 n + 47367) (n + 1) ----------------------------------------------------------------- 9 2 4 5 2 - 2240 (21 n + 39 n + 85) (n + 1) Hn[1] + 6720 (n + 1) Hn[1] 2 5 6 + (-4480 (21 n + 39 n + 50) (n + 1) + 26880 (n + 1) Hn[1]) Hn[2] \ 7 2| 6 2 + 26880 (n + 1) Hn[2] | Hn[3] - 53760 (n + 1) Hn[3] + ( / 3 2 4 5 3360 (19 n + 123 n + 182 n + 122) (n + 1) - 87360 (n + 1) Hn[1] 6 7 - 120960 (n + 1) Hn[2] - 53760 (n + 1) Hn[3]) Hn[4] + ( 2 5 6 5376 (21 n + 39 n + 50) (n + 1) - 32256 (n + 1) Hn[1] 7 6 - 64512 (n + 1) Hn[2]) Hn[5] + 161280 (n + 1) Hn[6] 7 7 6 + 92160 (n + 1) Hn[7], n (90558126238639 n + 874593379118567 n 5 4 3 + 3765950297083317 n + 9448880537396279 n + 15222514193079466 n 2 + 16203885880146258 n + 11083988704917328 n + 4441528864215146)/14883750 6 5 4 - 2/675 (n + 1) (519753619 n + 4227400499 n + 15454641825 n 3 2 + 31080886165 n + 38860221806 n + 28165993086 n + 10271667375) Hn[1] + 4 3 2 2 2 28/3 (22600 n + 128500 n + 429230 n + 544910 n + 559371) (n + 1) Hn[1] 2 3 3 4 4 - 560 (42 n + 78 n + 427) (n + 1) Hn[1] + 1680 (n + 1) Hn[1] + (- 4 ( 6 5 4 3 519753619 n + 3905931099 n + 12918002825 n + 23472392965 n 2 2 + 25572779106 n + 16029920186 n + 3808624725) (n + 1) /675 + 4 3 2 3 112/3 (22600 n + 119380 n + 337850 n + 397490 n + 305061) (n + 1) Hn[1] 2 4 2 5 3 - 1120 (126 n + 234 n + 919) (n + 1) Hn[1] + 13440 (n + 1) Hn[1] ) / | Hn[2] + | \ 4 3 2 4 112 (22600 n + 110260 n + 259910 n + 275030 n + 151227) (n + 1) ------------------------------------------------------------------- 3 \ 2 5 6 2| 2 - 20160 (14 n + 26 n + 69) (n + 1) Hn[1] + 40320 (n + 1) Hn[1] | Hn[2] / 6 7 3 + (-13440 %1 (n + 1) + 53760 (n + 1) Hn[1]) Hn[2] 8 4 + 26880 (n + 1) Hn[2] + (- 224 5 4 3 2 (229621 n + 1625435 n + 4444965 n + 6655195 n + 5310824 n + 1959795) 3 3 2 4 (n + 1) /27 + 896 (380 n + 3230 n + 5070 n + 6277) (n + 1) Hn[1] 5 2 - 331520 (n + 1) Hn[1] + 3 2 5 6 (8960 (76 n + 534 n + 806 n + 695) (n + 1) - 1039360 (n + 1) Hn[1]) 7 2 Hn[2] - 752640 (n + 1) Hn[2] ) Hn[3] + 6 7 8 2 (35840 %1 (n + 1) - 143360 (n + 1) Hn[1] - 286720 (n + 1) Hn[2]) Hn[3] / 4 3 2 4 | 224 (22600 n + 110260 n + 259910 n + 275030 n + 151227) (n + 1) + |- ------------------------------------------------------------------- \ 3 2 5 6 2 + 40320 (14 n + 26 n + 69) (n + 1) Hn[1] - 80640 (n + 1) Hn[1] 6 7 + (80640 %1 (n + 1) - 322560 (n + 1) Hn[1]) Hn[2] \ 8 2 7 | - 322560 (n + 1) Hn[2] + 1505280 (n + 1) Hn[3]| Hn[4] / 8 2 3 2 5 + 322560 (n + 1) Hn[4] + (-10752 (76 n + 534 n + 806 n + 695) (n + 1) 6 7 8 + 1247232 (n + 1) Hn[1] + 1806336 (n + 1) Hn[2] + 688128 (n + 1) Hn[3]) Hn[5] + 6 7 8 (-107520 %1 (n + 1) + 430080 (n + 1) Hn[1] + 860160 (n + 1) Hn[2]) Hn[6] 7 8 - 2580480 (n + 1) Hn[7] - 1290240 (n + 1) Hn[8]] 2 %1 := 14 n + 26 n + 43 and in Maple format [-4*n+Hn[1]*(2*n+2), n*(7*n+13)+Hn[1]*(-2*n-2)-4*(n+1)^2*Hn[2], -n*(19*n^2+81*n +104)+Hn[1]*(14*n+14)+12*(n+1)^2*Hn[2]+16*(n+1)^3*Hn[3], 1/9*n*(2260*n^3+9658*n ^2+15497*n+11357)-2*(n+1)*(42*n^2+78*n+77)*Hn[1]+12*(n+1)^2*Hn[1]^2+(-4*(42*n^2 +78*n+31)*(n+1)^2+48*(n+1)^3*Hn[1])*Hn[2]+48*(n+1)^4*Hn[2]^2-96*(n+1)^3*Hn[3]-\ 96*(n+1)^4*Hn[4], -1/108*n*(229621*n^4+1422035*n^3+3401325*n^2+3915865*n+ 2217794)+2*(n+1)*(190*n^3+1300*n^2+1950*n+1171)*Hn[1]-280*(n+1)^2*Hn[1]^2+(20*( 38*n^3+204*n^2+286*n+91)*(n+1)^2-800*(n+1)^3*Hn[1])*Hn[2]-480*(n+1)^4*Hn[2]^2+( 80*(14*n^2+26*n+17)*(n+1)^3-320*(n+1)^4*Hn[1]-640*(n+1)^5*Hn[2])*Hn[3]+960*(n+1 )^4*Hn[4]+768*(n+1)^5*Hn[5], 1/2700*n*(74250517*n^5+523547007*n^4+1579578725*n^ 3+2571768745*n^2+2342670258*n+1133389148)-2/3*(n+1)*(11300*n^4+56270*n^3+135760 *n^2+145510*n+68427)*Hn[1]+20*(63*n^2+117*n+329)*(n+1)^2*Hn[1]^2-120*(n+1)^3*Hn [1]^3+(-4/3*(11300*n^4+51710*n^3+101830*n^2+93640*n+26013)*(n+1)^2+240*(21*n^2+ 39*n+68)*(n+1)^3*Hn[1]-720*(n+1)^4*Hn[1]^2)*Hn[2]+(240*(21*n^2+39*n+37)*(n+1)^4 -1440*(n+1)^5*Hn[1])*Hn[2]^2-960*(n+1)^6*Hn[2]^3+(-160*(38*n^3+225*n^2+325*n+ 159)*(n+1)^3+7360*(n+1)^4*Hn[1]+9600*(n+1)^5*Hn[2])*Hn[3]+2560*(n+1)^6*Hn[3]^2+ (-480*(21*n^2+39*n+37)*(n+1)^4+2880*(n+1)^5*Hn[1]+5760*(n+1)^6*Hn[2])*Hn[4]-\ 11520*(n+1)^5*Hn[5]-7680*(n+1)^6*Hn[6], -7/81000*n*(4361821529*n^6+36987323153* n^5+135379990924*n^4+280732243290*n^3+356835588161*n^2+275702876557*n+ 119672624386)+1/18*(n+1)*(1607347*n^5+12169045*n^4+35117495*n^3+56653667*n^2+ 48253086*n+19517436)*Hn[1]-28*(285*n^3+2685*n^2+4290*n+6208)*(n+1)^2*Hn[1]^2+ 5880*(n+1)^3*Hn[1]^3+(7/9*(229621*n^5+1557635*n^4+4086825*n^3+5641645*n^2+ 4118354*n+1044612)*(n+1)^2-112*(285*n^3+2265*n^2+3510*n+3559)*(n+1)^3*Hn[1]+ 28560*(n+1)^4*Hn[1]^2)*Hn[2]+(-1680*(19*n^3+123*n^2+182*n+122)*(n+1)^4+43680*(n +1)^5*Hn[1])*Hn[2]^2+20160*(n+1)^6*Hn[2]^3+(112/9*(11300*n^4+53420*n^3+115420*n ^2+114700*n+47367)*(n+1)^3-2240*(21*n^2+39*n+85)*(n+1)^4*Hn[1]+6720*(n+1)^5*Hn[ 1]^2+(-4480*(21*n^2+39*n+50)*(n+1)^5+26880*(n+1)^6*Hn[1])*Hn[2]+26880*(n+1)^7* Hn[2]^2)*Hn[3]-53760*(n+1)^6*Hn[3]^2+(3360*(19*n^3+123*n^2+182*n+122)*(n+1)^4-\ 87360*(n+1)^5*Hn[1]-120960*(n+1)^6*Hn[2]-53760*(n+1)^7*Hn[3])*Hn[4]+(5376*(21*n ^2+39*n+50)*(n+1)^5-32256*(n+1)^6*Hn[1]-64512*(n+1)^7*Hn[2])*Hn[5]+161280*(n+1) ^6*Hn[6]+92160*(n+1)^7*Hn[7], 1/14883750*n*(90558126238639*n^7+874593379118567* n^6+3765950297083317*n^5+9448880537396279*n^4+15222514193079466*n^3+ 16203885880146258*n^2+11083988704917328*n+4441528864215146)-2/675*(n+1)*( 519753619*n^6+4227400499*n^5+15454641825*n^4+31080886165*n^3+38860221806*n^2+ 28165993086*n+10271667375)*Hn[1]+28/3*(22600*n^4+128500*n^3+429230*n^2+544910*n +559371)*(n+1)^2*Hn[1]^2-560*(42*n^2+78*n+427)*(n+1)^3*Hn[1]^3+1680*(n+1)^4*Hn[ 1]^4+(-4/675*(519753619*n^6+3905931099*n^5+12918002825*n^4+23472392965*n^3+ 25572779106*n^2+16029920186*n+3808624725)*(n+1)^2+112/3*(22600*n^4+119380*n^3+ 337850*n^2+397490*n+305061)*(n+1)^3*Hn[1]-1120*(126*n^2+234*n+919)*(n+1)^4*Hn[1 ]^2+13440*(n+1)^5*Hn[1]^3)*Hn[2]+(112/3*(22600*n^4+110260*n^3+259910*n^2+275030 *n+151227)*(n+1)^4-20160*(14*n^2+26*n+69)*(n+1)^5*Hn[1]+40320*(n+1)^6*Hn[1]^2)* Hn[2]^2+(-13440*(14*n^2+26*n+43)*(n+1)^6+53760*(n+1)^7*Hn[1])*Hn[2]^3+26880*(n+ 1)^8*Hn[2]^4+(-224/27*(229621*n^5+1625435*n^4+4444965*n^3+6655195*n^2+5310824*n +1959795)*(n+1)^3+896*(380*n^3+3230*n^2+5070*n+6277)*(n+1)^4*Hn[1]-331520*(n+1) ^5*Hn[1]^2+(8960*(76*n^3+534*n^2+806*n+695)*(n+1)^5-1039360*(n+1)^6*Hn[1])*Hn[2 ]-752640*(n+1)^7*Hn[2]^2)*Hn[3]+(35840*(14*n^2+26*n+43)*(n+1)^6-143360*(n+1)^7* Hn[1]-286720*(n+1)^8*Hn[2])*Hn[3]^2+(-224/3*(22600*n^4+110260*n^3+259910*n^2+ 275030*n+151227)*(n+1)^4+40320*(14*n^2+26*n+69)*(n+1)^5*Hn[1]-80640*(n+1)^6*Hn[ 1]^2+(80640*(14*n^2+26*n+43)*(n+1)^6-322560*(n+1)^7*Hn[1])*Hn[2]-322560*(n+1)^8 *Hn[2]^2+1505280*(n+1)^7*Hn[3])*Hn[4]+322560*(n+1)^8*Hn[4]^2+(-10752*(76*n^3+ 534*n^2+806*n+695)*(n+1)^5+1247232*(n+1)^6*Hn[1]+1806336*(n+1)^7*Hn[2]+688128*( n+1)^8*Hn[3])*Hn[5]+(-107520*(14*n^2+26*n+43)*(n+1)^6+430080*(n+1)^7*Hn[1]+ 860160*(n+1)^8*Hn[2])*Hn[6]-2580480*(n+1)^7*Hn[7]-1290240*(n+1)^8*Hn[8]] This is asymptotically / 2\ | 2 Pi | 2 [(-4 + 2 ln(n) + 2 gamma) n + 2 ln(n) + 2 gamma, |7 - -----| n \ 3 / / 2\ 2 | 4 Pi | 2 Pi + |13 - 2 ln(n) - 2 gamma - -----| n - 2 ln(n) - 2 gamma - -----, \ 3 / 3 3 2 2 (-19 + 16 Zeta(3)) n + (-81 + 2 Pi + 48 Zeta(3)) n 2 + (-104 + 14 ln(n) + 14 gamma + 4 Pi + 48 Zeta(3)) n + 14 ln(n) / 2 2 4 4 | + 14 gamma + 2 Pi + 16 Zeta(3), (2260/9 - 28 Pi + 4/15 Pi ) n + |9658/9 \ 4 2 16 Pi - 84 ln(n) - 84 gamma + 1/6 (-648 + 48 ln(n) + 48 gamma) Pi + ------ 15 \ / | 3 | 2 - 96 Zeta(3)| n + |15497/9 - 240 ln(n) - 240 gamma + 12 (ln(n) + gamma) / \ 4 \ / 2 8 Pi | 2 | + 1/6 (-916 + 144 ln(n) + 144 gamma) Pi + ----- - 288 Zeta(3)| n + | 5 / \ 2 11357/9 - 310 ln(n) - 310 gamma + 24 (ln(n) + gamma) 4 \ 2 16 Pi | + 1/6 (-560 + 144 ln(n) + 144 gamma) Pi + ------ - 288 Zeta(3)| n 15 / 2 - 154 ln(n) - 154 gamma + 12 (ln(n) + gamma) 4 2 4 Pi + 1/6 (-124 + 48 ln(n) + 48 gamma) Pi + ----- - 96 Zeta(3), 15 / 2 / 2\ \ / | 229621 380 Pi | 320 Pi | | 5 | |- ------ + ------- + |1120 - -------| Zeta(3) + 768 Zeta(5)| n + | \ 108 3 \ 3 / / \ 2 4 1422035 2800 Pi 8 Pi - ------- + 380 ln(n) + 380 gamma + -------- - ----- 108 3 3 / 2\ \ / | 1600 Pi | | 4 | + |5440 - 320 ln(n) - 320 gamma - --------| Zeta(3) + 3840 Zeta(5)| n + | \ 3 / / \ - 125975/4 + 2980 ln(n) + 2980 gamma 4 2 32 Pi + 1/6 (14640 - 800 ln(n) - 800 gamma) Pi - ------ 3 / 2\ \ | 3200 Pi | | 3 + |10960 - 1280 ln(n) - 1280 gamma - --------| Zeta(3) + 7680 Zeta(5)| n \ 3 / / / | 3915865 2 + |- ------- + 6500 ln(n) + 6500 gamma - 280 (ln(n) + gamma) \ 108 2 4 + 1/6 (17340 - 2400 ln(n) - 2400 gamma) Pi - 16 Pi / 2\ \ | 3200 Pi | | 2 + |11440 - 1920 ln(n) - 1920 gamma - --------| Zeta(3) + 7680 Zeta(5)| n \ 3 / / / | 1108897 2 + |- ------- + 6242 ln(n) + 6242 gamma - 560 (ln(n) + gamma) \ 54 4 2 32 Pi + 1/6 (9360 - 2400 ln(n) - 2400 gamma) Pi - ------ 3 / 2\ \ | 1600 Pi | | + |6160 - 1280 ln(n) - 1280 gamma - --------| Zeta(3) + 3840 Zeta(5)| n \ 3 / / 2 + 2342 ln(n) + 2342 gamma - 280 (ln(n) + gamma) 4 2 8 Pi + 1/6 (1820 - 800 ln(n) - 800 gamma) Pi - ----- 3 / 2\ / | 320 Pi | | + |1360 - 320 ln(n) - 320 gamma - -------| Zeta(3) + 768 Zeta(5), | \ 3 / \ 2 6 74250517 22600 Pi 4 88 Pi 2 -------- - --------- + 140 Pi - ------ - 6080 Zeta(3) + 2560 Zeta(3) 2700 9 7 2 4\ / (960 Pi - 10080) Pi | 6 |174515669 22600 gamma + ---------------------| n + |--------- - 22600/3 ln(n) - ----------- 90 / \ 900 3 2 + 1/6 (-99080 + 5040 ln(n) + 5040 gamma) Pi 6 4 528 Pi + 1/36 (29520 - 1440 ln(n) - 1440 gamma) Pi - ------- 7 2 2 + (1600 Pi - 54240) Zeta(3) + 15360 Zeta(3) \ 2 4 | + 1/90 (5760 Pi + 2880 ln(n) + 2880 gamma - 59040) Pi - 11520 Zeta(5)| / / 5 |63183149 135140 gamma 2 n + |-------- - 135140/3 ln(n) - ------------ + 1260 (ln(n) + gamma) \ 108 3 2 2 + 1/6 (- 866200/3 + 24480 ln(n) + 24480 gamma - 720 (ln(n) + gamma) ) Pi 6 4 1320 Pi + 1/36 (76560 - 7200 ln(n) - 7200 gamma) Pi - -------- 7 2 2 + (8000 Pi + 7360 ln(n) + 7360 gamma - 178240) Zeta(3) + 38400 Zeta(3) 2 4 + 1/90 (14400 Pi + 14400 ln(n) + 14400 gamma - 153120) Pi \ / | 4 |514353749 - 57600 Zeta(5)| n + |--------- - 128020 ln(n) - 128020 gamma / \ 540 2 3 + 4860 (ln(n) + gamma) - 120 (ln(n) + gamma) + 2 2 1/6 (- 1396040/3 + 59520 ln(n) + 59520 gamma - 2880 (ln(n) + gamma) ) Pi 6 4 1760 Pi + 1/36 (111840 - 14400 ln(n) - 14400 gamma) Pi - -------- 7 2 + (16000 Pi + 29440 ln(n) + 29440 gamma - 295520) Zeta(3) 2 + 51200 Zeta(3) 2 4 + 1/90 (19200 Pi + 28800 ln(n) + 28800 gamma - 223680) Pi \ / | 3 |390445043 562540 gamma - 115200 Zeta(5)| n + |--------- - 562540/3 ln(n) - ------------ / \ 450 3 2 3 + 12520 (ln(n) + gamma) - 360 (ln(n) + gamma) 2 2 + 1/6 (-4320 (ln(n) + gamma) + 82080 ln(n) + 82080 gamma - 420164) Pi 6 4 1320 Pi + 1/36 (95760 - 14400 ln(n) - 14400 gamma) Pi - -------- 7 2 + (16000 Pi + 44160 ln(n) + 44160 gamma - 268320) Zeta(3) 2 + 38400 Zeta(3) 2 4 + 1/90 (14400 Pi + 28800 ln(n) + 28800 gamma - 191520) Pi \ / | 2 |283347287 427874 gamma - 115200 Zeta(5)| n + |--------- - 427874/3 ln(n) - ------------ / \ 675 3 2 3 + 15500 (ln(n) + gamma) - 360 (ln(n) + gamma) 2 2 + 1/6 (- 582664/3 + 58320 ln(n) + 58320 gamma - 2880 (ln(n) + gamma) ) Pi 6 4 528 Pi + 1/36 (44880 - 7200 ln(n) - 7200 gamma) Pi - ------- 7 2 2 + (8000 Pi + 29440 ln(n) + 29440 gamma - 128320) Zeta(3) + 15360 Zeta(3) \ 2 4 | + 1/90 (5760 Pi + 14400 ln(n) + 14400 gamma - 89760) Pi - 57600 Zeta(5)| / 2 n - 45618 ln(n) - 45618 gamma + 6580 (ln(n) + gamma) 3 - 120 (ln(n) + gamma) 2 2 + 1/6 (-720 (ln(n) + gamma) + 16320 ln(n) + 16320 gamma - 34684) Pi 6 4 88 Pi + 1/36 (8880 - 1440 ln(n) - 1440 gamma) Pi - ------ 7 2 2 + (1600 Pi + 7360 ln(n) + 7360 gamma - 25440) Zeta(3) + 2560 Zeta(3) / 2 4 | + 1/90 (960 Pi + 2880 ln(n) + 2880 gamma - 17760) Pi - 11520 Zeta(5), | \ 2 4 30532750703 1607347 Pi 2660 Pi - ----------- + ----------- - -------- 81000 54 3 2 4 + (1265600/9 - 15680 Pi + 2240/3 Pi ) Zeta(3) 4 2 + 1/90 (63840 - 53760 Zeta(3)) Pi + (-10752 Pi + 112896) Zeta(5) \ / | 7 | 258911262071 1607347 1607347 gamma + 92160 Zeta(7)| n + |- ------------ + ------- ln(n) + ------------- / \ 81000 18 18 4 2 27860 Pi 6 + 1/6 (14118139/9 - 31920 ln(n) - 31920 gamma) Pi - --------- + 264 Pi 3 / | + |9779840/9 - 47040 ln(n) - 47040 gamma \ 4\ 2 15680 Pi | + 1/6 (-645120 + 26880 ln(n) + 26880 gamma) Pi + ---------| Zeta(3) 3 / 2 2 4 - 53760 Zeta(3) + 1/90 (668640 - 20160 Pi - 376320 Zeta(3)) Pi 2 + (-75264 Pi - 32256 ln(n) - 32256 gamma + 774144) Zeta(5) \ | 6 / 236914984117 6888196 gamma + 645120 Zeta(7)| n + |- ------------ + 6888196/9 ln(n) + ------------- / \ 20250 9 2 - 7980 (ln(n) + gamma) 2 + 1/6 (52022012/9 - 349440 ln(n) - 349440 gamma) Pi 4 6 + 1/36 (-1323840 + 43680 ln(n) + 43680 gamma) Pi + 1584 Pi + (34672960/9 2 - 275520 ln(n) - 275520 gamma + 6720 (ln(n) + gamma) 2 4 + 1/6 (-2038400 + 161280 ln(n) + 161280 gamma) Pi + 15680 Pi ) Zeta(3) 2 - 322560 Zeta(3) + 1/90 2 4 (2647680 - 87360 ln(n) - 87360 gamma - 120960 Pi - 1128960 Zeta(3)) Pi 2 + (-225792 Pi - 193536 ln(n) - 193536 gamma + 2446080) Zeta(5) / \ 5 | 65504190101 + 1935360 Zeta(7)| n + |- ----------- + 2627030 ln(n) + 2627030 gamma / \ 2700 2 - 91140 (ln(n) + gamma) + 1/6 2 2 (35870170/3 - 1249920 ln(n) - 1249920 gamma + 28560 (ln(n) + gamma) ) Pi / 4 6 | + 1/36 (-2795520 + 218400 ln(n) + 218400 gamma) Pi + 3960 Pi + |7871360 \ 2 - 822080 ln(n) - 822080 gamma + 33600 (ln(n) + gamma) 4\ 2 78400 Pi | + 1/6 (-3808000 + 403200 ln(n) + 403200 gamma) Pi + ---------| Zeta(3) 3 / 2 - 806400 Zeta(3) + 1/90 2 4 (5591040 - 436800 ln(n) - 436800 gamma - 302400 Pi - 1881600 Zeta(3)) Pi 2 + (-376320 Pi - 483840 ln(n) - 483840 gamma + 4569600) Zeta(5) \ / | 4 | 2497849117127 + 3225600 Zeta(7)| n + |- ------------- + 45885581/9 ln(n) / \ 81000 45885581 gamma 2 3 + -------------- - 278460 (ln(n) + gamma) + 5880 (ln(n) + gamma) + 1/6 9 2 2 (136419283/9 - 2370928 ln(n) - 2370928 gamma + 114240 (ln(n) + gamma) ) Pi / 4 6 | + 1/36 (-3512880 + 436800 ln(n) + 436800 gamma) Pi + 5280 Pi + | \ 2 88608464/9 - 1473920 ln(n) - 1473920 gamma + 67200 (ln(n) + gamma) 4\ 2 78400 Pi | + 1/6 (-4457600 + 537600 ln(n) + 537600 gamma) Pi + ---------| Zeta(3) 3 / 2 - 1075200 Zeta(3) + 1/90 2 4 (7025760 - 873600 ln(n) - 873600 gamma - 403200 Pi - 1881600 Zeta(3)) Pi 2 + (-376320 Pi - 645120 ln(n) - 645120 gamma + 5349120) Zeta(5) \ | 3 / 1929920135899 104906753 + 3225600 Zeta(7)| n + |- ------------- + --------- ln(n) / \ 81000 18 104906753 gamma 2 3 + --------------- - 489244 (ln(n) + gamma) + 17640 (ln(n) + gamma) + 1/6 18 2 2 (104460755/9 - 2628864 ln(n) - 2628864 gamma + 171360 (ln(n) + gamma) ) Pi 4 6 + 1/36 (-2659440 + 436800 ln(n) + 436800 gamma) Pi + 3960 Pi + ( 2 67381552/9 - 1538880 ln(n) - 1538880 gamma + 67200 (ln(n) + gamma) 2 4 + 1/6 (-3207680 + 403200 ln(n) + 403200 gamma) Pi + 15680 Pi ) Zeta(3) 2 - 806400 Zeta(3) + 1/90 2 4 (5318880 - 873600 ln(n) - 873600 gamma - 302400 Pi - 1128960 Zeta(3)) Pi 2 + (-225792 Pi - 483840 ln(n) - 483840 gamma + 3849216) Zeta(5) / \ 2 | 418854185351 + 1935360 Zeta(7)| n + |- ------------ + 3765029 ln(n) + 3765029 gamma / \ 40500 2 3 - 467768 (ln(n) + gamma) + 17640 (ln(n) + gamma) + 1/6 2 2 (43453046/9 - 1588944 ln(n) - 1588944 gamma + 114240 (ln(n) + gamma) ) Pi / 4 6 | + 1/36 (-1125600 + 218400 ln(n) + 218400 gamma) Pi + 1584 Pi + | \ 2 28761712/9 - 848960 ln(n) - 848960 gamma + 33600 (ln(n) + gamma) 4\ 2 15680 Pi | + 1/6 (-1294720 + 161280 ln(n) + 161280 gamma) Pi + ---------| Zeta(3) 3 / 2 - 322560 Zeta(3) + 1/90 2 4 (2251200 - 436800 ln(n) - 436800 gamma - 120960 Pi - 376320 Zeta(3)) Pi 2 + (-75264 Pi - 193536 ln(n) - 193536 gamma + 1553664) Zeta(5) \ | + 645120 Zeta(7)| n + 1084302 ln(n) + 1084302 gamma / 2 3 - 173824 (ln(n) + gamma) + 5880 (ln(n) + gamma) 2 2 + 1/6 (28560 (ln(n) + gamma) - 398608 ln(n) - 398608 gamma + 812476) Pi / 4 6 | + 1/36 (-204960 + 43680 ln(n) + 43680 gamma) Pi + 264 Pi + |589456 \ 2 - 190400 ln(n) - 190400 gamma + 6720 (ln(n) + gamma) 4\ 2 2240 Pi | + 1/6 (-224000 + 26880 ln(n) + 26880 gamma) Pi + --------| Zeta(3) 3 / 2 - 53760 Zeta(3) + 2 4 1/90 (409920 - 87360 ln(n) - 87360 gamma - 20160 Pi - 53760 Zeta(3)) Pi 2 + (-10752 Pi - 32256 ln(n) - 32256 gamma + 268800) Zeta(5) / 2 4 6 |90558126238639 1039507238 Pi 632800 Pi 7840 Pi + 92160 Zeta(7), |-------------- - -------------- + ---------- - -------- \ 14883750 2025 27 9 8 / 2\ 10256 Pi | 51435104 340480 Pi | - --------- + |- -------- + ----------| Zeta(3) 135 \ 27 3 / / 2\ | 143360 Pi | 2 + |501760 - ----------| Zeta(3) \ 3 / 2 4 4 (- 5062400/3 + 188160 Pi - 8960 Pi ) Pi + ----------------------------------------- 90 2 6\ / (143360 Pi - 1505280) Pi | 8 | + (-817152 + 688128 Zeta(3)) Zeta(5) + --------------------------| n + | 945 / \ 874593379118567 1039507238 1039507238 gamma --------------- - ---------- ln(n) - ---------------- 14883750 675 675 / 19781753348 2531200 gamma\ 2 + 1/6 |- ----------- + 2531200/3 ln(n) + -------------| Pi \ 675 3 / 4 + 1/36 (22473920/3 - 282240 ln(n) - 282240 gamma) Pi 8 6 82048 Pi + 1/216 (-1478400 + 53760 ln(n) + 53760 gamma) Pi - --------- + 135 / 2 4\ | 518402752 4094720 Pi 62720 Pi | |- --------- + 340480 ln(n) + 340480 gamma + ----------- - ---------| \ 27 3 3 / / 2\ | 1146880 Pi | 2 Zeta(3) + |3942400 - 143360 ln(n) - 143360 gamma - -----------| Zeta(3) + \ 3 / 1/90 (- 44947840/3 + 564480 ln(n) + 564480 gamma 2 4 + 1/6 (8870400 - 322560 ln(n) - 322560 gamma) Pi - 71680 Pi 4 2 + 1505280 Zeta(3)) Pi + (-9827328 + 301056 Pi + 5505024 Zeta(3)) Zeta(5) 2 6 + 1/945 (1146880 Pi + 430080 ln(n) + 430080 gamma - 11827200) Pi \ / | 7 |179330966527777 3164769412 - 2580480 Zeta(7)| n + |--------------- - ---------- ln(n) / \ 708750 225 3164769412 gamma 2 / - ---------------- + 632800/3 (ln(n) + gamma) + 1/6 | 225 \ 9444274952 20964160 gamma 2\ - ---------- + 20964160/3 ln(n) + -------------- - 141120 (ln(n) + gamma) | 75 3 / 2 Pi + 1/36 2 4 (40320 (ln(n) + gamma) - 1935360 ln(n) - 1935360 gamma + 31231200) Pi 8 / 6 287168 Pi | + 1/216 (-5496960 + 376320 ln(n) + 376320 gamma) Pi - ---------- + | 135 \ - 249141088/3 + 4256000 ln(n) + 4256000 gamma 4\ 2 439040 Pi | + 1/6 (37954560 - 1039360 ln(n) - 1039360 gamma) Pi - ----------| Zeta(3) 3 / / 2\ | 4014080 Pi | 2 + |14658560 - 1003520 ln(n) - 1003520 gamma - -----------| Zeta(3) + 1/90 \ 3 / 2 (-62462400 + 3870720 ln(n) + 3870720 gamma - 80640 (ln(n) + gamma) 2 4 + 1/6 (32981760 - 2257920 ln(n) - 2257920 gamma) Pi - 250880 Pi 4 + 10536960 Zeta(3)) Pi + ( 2 -45545472 + 1247232 ln(n) + 1247232 gamma + 2107392 Pi + 19267584 Zeta(3)) Zeta(5) 2 6 + 1/945 (4014080 Pi + 3010560 ln(n) + 3010560 gamma - 43975680) Pi \ / | 6 |1349840076770897 39364084648 - 18063360 Zeta(7)| n + |---------------- - ----------- ln(n) / \ 2126250 675 39364084648 gamma 2 3 - ----------------- + 1621200 (ln(n) + gamma) - 23520 (ln(n) + gamma) + 675 / 212857318856 85544480 gamma 1/6 |- ------------ + 85544480/3 ln(n) + -------------- \ 675 3 2 3\ 2 - 826560 (ln(n) + gamma) + 13440 (ln(n) + gamma) | Pi + 1/36 / 2 4 (231462560/3 - 6834240 ln(n) - 6834240 gamma + 241920 (ln(n) + gamma) ) Pi 8 6 574336 Pi / + 1/216 (-12472320 + 1128960 ln(n) + 1128960 gamma) Pi - ---------- + | 135 \ 5621507584 2 - ---------- + 18161920 ln(n) + 18161920 gamma - 331520 (ln(n) + gamma) 27 2 4\ + 1/6 (96992000 - 6236160 ln(n) - 6236160 gamma) Pi - 439040 Pi | Zeta(3) / / 2\ | 8028160 Pi | 2 + |33259520 - 3010560 ln(n) - 3010560 gamma - -----------| Zeta(3) + 1/90 \ 3 / 2 (- 462925120/3 + 13668480 ln(n) + 13668480 gamma - 483840 (ln(n) + gamma) 2 4 + 1/6 (74833920 - 6773760 ln(n) - 6773760 gamma) Pi - 501760 Pi 4 + 31610880 Zeta(3)) Pi + ( 2 -116390400 + 7483392 ln(n) + 7483392 gamma + 6322176 Pi + 38535168 Zeta(3) ) Zeta(5) 2 6 + 1/945 (8028160 Pi + 9031680 ln(n) + 9031680 gamma - 99778560) Pi \ / | 5 |1087322442362819 18614211196 - 54190080 Zeta(7)| n + |---------------- - ----------- ln(n) / \ 1063125 135 18614211196 gamma 2 - ----------------- + 19847240/3 (ln(n) + gamma) 135 3 4 / 341742271444 - 114240 (ln(n) + gamma) + 1680 (ln(n) + gamma) + 1/6 |- ------------ \ 675 2 + 66893120 ln(n) + 66893120 gamma - 2924320 (ln(n) + gamma) 3\ 2 + 67200 (ln(n) + gamma) | Pi + 1/36 / 2 (366738064/3 - 15019200 ln(n) - 15019200 gamma + 604800 (ln(n) + gamma) ) 8 4 6 143584 Pi Pi + 1/216 (-18480000 + 1881600 ln(n) + 1881600 gamma) Pi - ---------- + 27 / | 9013029536 2 |- ---------- + 42521472 ln(n) + 42521472 gamma - 1657600 (ln(n) + gamma) \ 27 4\ 2 2195200 Pi | + 1/6 (154604800 - 15590400 ln(n) - 15590400 gamma) Pi - -----------| 3 / Zeta(3) / 2\ | 10035200 Pi | 2 + |49280000 - 5017600 ln(n) - 5017600 gamma - ------------| Zeta(3) + \ 3 / 1/90 (- 733476128/3 + 30038400 ln(n) + 30038400 gamma 2 - 1209600 (ln(n) + gamma) 2 4 + 1/6 (110880000 - 11289600 ln(n) - 11289600 gamma) Pi - 627200 Pi 4 + 52684800 Zeta(3)) Pi + (-185525760 + 18708480 ln(n) + 18708480 gamma 2 + 10536960 Pi + 48168960 Zeta(3)) Zeta(5) 2 6 + 1/945 (10035200 Pi + 15052800 ln(n) + 15052800 gamma - 147840000) Pi \ / | 4 |385806806670149 15542468438 - 90316800 Zeta(7)| n + |--------------- - ----------- ln(n) / \ 354375 75 15542468438 gamma 2 - ----------------- + 42892360/3 (ln(n) + gamma) 75 3 4 / 13429314276 - 440720 (ln(n) + gamma) + 6720 (ln(n) + gamma) + 1/6 |- ----------- \ 25 294611632 gamma 2 + 294611632/3 ln(n) + --------------- - 6254080 (ln(n) + gamma) 3 3\ 2 + 134400 (ln(n) + gamma) | Pi + 1/36 / 2 4 (806400 (ln(n) + gamma) - 20563200 ln(n) - 20563200 gamma + 127119552) Pi 8 / 6 574336 Pi | + 1/216 (-17928960 + 1881600 ln(n) + 1881600 gamma) Pi - ---------- + | 135 \ 2 -350956704 + 61669888 ln(n) + 61669888 gamma - 3315200 (ln(n) + gamma) 4\ 2 2195200 Pi | + 1/6 (159093760 - 20787200 ln(n) - 20787200 gamma) Pi - -----------| 3 / / 2\ | 8028160 Pi | 2 Zeta(3) + |47810560 - 5017600 ln(n) - 5017600 gamma - -----------| Zeta(3) \ 3 / + 1/90 (-254239104 + 41126400 ln(n) + 41126400 gamma 2 - 1612800 (ln(n) + gamma) 2 4 + 1/6 (107573760 - 11289600 ln(n) - 11289600 gamma) Pi - 501760 Pi 4 + 52684800 Zeta(3)) Pi + (-190912512 + 24944640 ln(n) + 24944640 gamma 2 + 10536960 Pi + 38535168 Zeta(3)) Zeta(5) 2 6 + 1/945 (8028160 Pi + 15052800 ln(n) + 15052800 gamma - 143431680) Pi \ / | 3 |5541994352458664 134052429784 - 90316800 Zeta(7)| n + |---------------- - ------------ ln(n) / \ 7441875 675 134052429784 gamma 2 3 - ------------------ + 19398596 (ln(n) + gamma) - 871920 (ln(n) + gamma) 675 4 / 245764976812 + 10080 (ln(n) + gamma) + 1/6 |- ------------ + 273896336/3 ln(n) \ 675 273896336 gamma 2 3\ + --------------- - 7365120 (ln(n) + gamma) + 134400 (ln(n) + gamma) | 3 / 2 Pi + 1/36 2 (253947904/3 - 16813440 ln(n) - 16813440 gamma + 604800 (ln(n) + gamma) ) 8 4 6 287168 Pi Pi + 1/216 (-10953600 + 1128960 ln(n) + 1128960 gamma) Pi - ---------- + 135 / 6376619648 2 |- ---------- + 54810112 ln(n) + 54810112 gamma - 3315200 (ln(n) + gamma) \ 27 2 4\ + 1/6 (103165440 - 15590400 ln(n) - 15590400 gamma) Pi - 439040 Pi | / / 2\ | 4014080 Pi | 2 Zeta(3) + |29209600 - 3010560 ln(n) - 3010560 gamma - -----------| Zeta(3) \ 3 / + 1/90 (- 507895808/3 + 33626880 ln(n) + 33626880 gamma 2 - 1209600 (ln(n) + gamma) 2 4 + 1/6 (65721600 - 6773760 ln(n) - 6773760 gamma) Pi - 250880 Pi 4 + 31610880 Zeta(3)) Pi + (-123798528 + 18708480 ln(n) + 18708480 gamma 2 + 6322176 Pi + 19267584 Zeta(3)) Zeta(5) 2 6 + 1/945 (4014080 Pi + 9031680 ln(n) + 9031680 gamma - 87628800) Pi \ / | 2 |2220764432107573 25625106974 - 54190080 Zeta(7)| n + |---------------- - ----------- ln(n) / \ 7441875 225 25625106974 gamma 2 - ----------------- + 46582256/3 (ln(n) + gamma) 225 3 4 / 94588678544 - 761040 (ln(n) + gamma) + 6720 (ln(n) + gamma) + 1/6 |- ----------- \ 675 147019376 gamma 2 + 147019376/3 ln(n) + --------------- - 4379200 (ln(n) + gamma) 3 3\ 2 + 67200 (ln(n) + gamma) | Pi + 1/36 / 2 4 (98553056/3 - 7479360 ln(n) - 7479360 gamma + 241920 (ln(n) + gamma) ) Pi 8 / 6 82048 Pi | + 1/216 (-3816960 + 376320 ln(n) + 376320 gamma) Pi - --------- + | 135 \ 2506606816 2 - ---------- + 27039488 ln(n) + 27039488 gamma - 1657600 (ln(n) + gamma) 27 4\ 2 439040 Pi | + 1/6 (38357760 - 6236160 ln(n) - 6236160 gamma) Pi - ----------| Zeta(3) 3 / / 2\ | 1146880 Pi | 2 + |10178560 - 1003520 ln(n) - 1003520 gamma - -----------| Zeta(3) + 1/90 \ 3 / 2 (- 197106112/3 + 14958720 ln(n) + 14958720 gamma - 483840 (ln(n) + gamma) 2 4 + 1/6 (22901760 - 2257920 ln(n) - 2257920 gamma) Pi - 71680 Pi 4 + 10536960 Zeta(3)) Pi + 2 (-46029312 + 7483392 ln(n) + 7483392 gamma + 2107392 Pi + 5505024 Zeta(3)) Zeta(5) 2 6 + 1/945 (1146880 Pi + 3010560 ln(n) + 3010560 gamma - 30535680) Pi \ | - 18063360 Zeta(7)| n - 30434570 ln(n) - 30434570 gamma / 2 3 + 5220796 (ln(n) + gamma) - 239120 (ln(n) + gamma) 4 3 + 1680 (ln(n) + gamma) + 1/6 (13440 (ln(n) + gamma) 2 - 1029280 (ln(n) + gamma) + 11388944 ln(n) + 11388944 gamma - 22569628) 2 Pi + 2 4 1/36 (40320 (ln(n) + gamma) - 1391040 ln(n) - 1391040 gamma + 5645808) Pi 8 / 6 10256 Pi | + 1/216 (-577920 + 53760 ln(n) + 53760 gamma) Pi - --------- + |-16259040 135 \ 2 + 5624192 ln(n) + 5624192 gamma - 331520 (ln(n) + gamma) 4\ 2 62720 Pi | + 1/6 (6227200 - 1039360 ln(n) - 1039360 gamma) Pi - ---------| Zeta(3) 3 / / 2\ | 143360 Pi | 2 + |1541120 - 143360 ln(n) - 143360 gamma - ----------| Zeta(3) + 1/90 ( \ 3 / 2 -11291616 + 2782080 ln(n) + 2782080 gamma - 80640 (ln(n) + gamma) 2 4 + 1/6 (3467520 - 322560 ln(n) - 322560 gamma) Pi - 8960 Pi 4 + 1505280 Zeta(3)) Pi + 2 (-7472640 + 1247232 ln(n) + 1247232 gamma + 301056 Pi + 688128 Zeta(3)) 2 6 Zeta(5) + 1/945 (143360 Pi + 430080 ln(n) + 430080 gamma - 4623360) Pi - 2580480 Zeta(7)] and in Maple format [(-4+2*ln(n)+2*gamma)*n+2*ln(n)+2*gamma, (7-2/3*Pi^2)*n^2+(13-2*ln(n)-2*gamma-4 /3*Pi^2)*n-2*ln(n)-2*gamma-2/3*Pi^2, (-19+16*Zeta(3))*n^3+(-81+2*Pi^2+48*Zeta(3 ))*n^2+(-104+14*ln(n)+14*gamma+4*Pi^2+48*Zeta(3))*n+14*ln(n)+14*gamma+2*Pi^2+16 *Zeta(3), (2260/9-28*Pi^2+4/15*Pi^4)*n^4+(9658/9-84*ln(n)-84*gamma+1/6*(-648+48 *ln(n)+48*gamma)*Pi^2+16/15*Pi^4-96*Zeta(3))*n^3+(15497/9-240*ln(n)-240*gamma+ 12*(ln(n)+gamma)^2+1/6*(-916+144*ln(n)+144*gamma)*Pi^2+8/5*Pi^4-288*Zeta(3))*n^ 2+(11357/9-310*ln(n)-310*gamma+24*(ln(n)+gamma)^2+1/6*(-560+144*ln(n)+144*gamma )*Pi^2+16/15*Pi^4-288*Zeta(3))*n-154*ln(n)-154*gamma+12*(ln(n)+gamma)^2+1/6*(-\ 124+48*ln(n)+48*gamma)*Pi^2+4/15*Pi^4-96*Zeta(3), (-229621/108+380/3*Pi^2+(1120 -320/3*Pi^2)*Zeta(3)+768*Zeta(5))*n^5+(-1422035/108+380*ln(n)+380*gamma+2800/3* Pi^2-8/3*Pi^4+(5440-320*ln(n)-320*gamma-1600/3*Pi^2)*Zeta(3)+3840*Zeta(5))*n^4+ (-125975/4+2980*ln(n)+2980*gamma+1/6*(14640-800*ln(n)-800*gamma)*Pi^2-32/3*Pi^4 +(10960-1280*ln(n)-1280*gamma-3200/3*Pi^2)*Zeta(3)+7680*Zeta(5))*n^3+(-3915865/ 108+6500*ln(n)+6500*gamma-280*(ln(n)+gamma)^2+1/6*(17340-2400*ln(n)-2400*gamma) *Pi^2-16*Pi^4+(11440-1920*ln(n)-1920*gamma-3200/3*Pi^2)*Zeta(3)+7680*Zeta(5))*n ^2+(-1108897/54+6242*ln(n)+6242*gamma-560*(ln(n)+gamma)^2+1/6*(9360-2400*ln(n)-\ 2400*gamma)*Pi^2-32/3*Pi^4+(6160-1280*ln(n)-1280*gamma-1600/3*Pi^2)*Zeta(3)+ 3840*Zeta(5))*n+2342*ln(n)+2342*gamma-280*(ln(n)+gamma)^2+1/6*(1820-800*ln(n)-\ 800*gamma)*Pi^2-8/3*Pi^4+(1360-320*ln(n)-320*gamma-320/3*Pi^2)*Zeta(3)+768*Zeta (5), (74250517/2700-22600/9*Pi^2+140*Pi^4-88/7*Pi^6-6080*Zeta(3)+2560*Zeta(3)^2 +1/90*(960*Pi^2-10080)*Pi^4)*n^6+(174515669/900-22600/3*ln(n)-22600/3*gamma+1/6 *(-99080+5040*ln(n)+5040*gamma)*Pi^2+1/36*(29520-1440*ln(n)-1440*gamma)*Pi^4-\ 528/7*Pi^6+(1600*Pi^2-54240)*Zeta(3)+15360*Zeta(3)^2+1/90*(5760*Pi^2+2880*ln(n) +2880*gamma-59040)*Pi^4-11520*Zeta(5))*n^5+(63183149/108-135140/3*ln(n)-135140/ 3*gamma+1260*(ln(n)+gamma)^2+1/6*(-866200/3+24480*ln(n)+24480*gamma-720*(ln(n)+ gamma)^2)*Pi^2+1/36*(76560-7200*ln(n)-7200*gamma)*Pi^4-1320/7*Pi^6+(8000*Pi^2+ 7360*ln(n)+7360*gamma-178240)*Zeta(3)+38400*Zeta(3)^2+1/90*(14400*Pi^2+14400*ln (n)+14400*gamma-153120)*Pi^4-57600*Zeta(5))*n^4+(514353749/540-128020*ln(n)-\ 128020*gamma+4860*(ln(n)+gamma)^2-120*(ln(n)+gamma)^3+1/6*(-1396040/3+59520*ln( n)+59520*gamma-2880*(ln(n)+gamma)^2)*Pi^2+1/36*(111840-14400*ln(n)-14400*gamma) *Pi^4-1760/7*Pi^6+(16000*Pi^2+29440*ln(n)+29440*gamma-295520)*Zeta(3)+51200* Zeta(3)^2+1/90*(19200*Pi^2+28800*ln(n)+28800*gamma-223680)*Pi^4-115200*Zeta(5)) *n^3+(390445043/450-562540/3*ln(n)-562540/3*gamma+12520*(ln(n)+gamma)^2-360*(ln (n)+gamma)^3+1/6*(-4320*(ln(n)+gamma)^2+82080*ln(n)+82080*gamma-420164)*Pi^2+1/ 36*(95760-14400*ln(n)-14400*gamma)*Pi^4-1320/7*Pi^6+(16000*Pi^2+44160*ln(n)+ 44160*gamma-268320)*Zeta(3)+38400*Zeta(3)^2+1/90*(14400*Pi^2+28800*ln(n)+28800* gamma-191520)*Pi^4-115200*Zeta(5))*n^2+(283347287/675-427874/3*ln(n)-427874/3* gamma+15500*(ln(n)+gamma)^2-360*(ln(n)+gamma)^3+1/6*(-582664/3+58320*ln(n)+ 58320*gamma-2880*(ln(n)+gamma)^2)*Pi^2+1/36*(44880-7200*ln(n)-7200*gamma)*Pi^4-\ 528/7*Pi^6+(8000*Pi^2+29440*ln(n)+29440*gamma-128320)*Zeta(3)+15360*Zeta(3)^2+1 /90*(5760*Pi^2+14400*ln(n)+14400*gamma-89760)*Pi^4-57600*Zeta(5))*n-45618*ln(n) -45618*gamma+6580*(ln(n)+gamma)^2-120*(ln(n)+gamma)^3+1/6*(-720*(ln(n)+gamma)^2 +16320*ln(n)+16320*gamma-34684)*Pi^2+1/36*(8880-1440*ln(n)-1440*gamma)*Pi^4-88/ 7*Pi^6+(1600*Pi^2+7360*ln(n)+7360*gamma-25440)*Zeta(3)+2560*Zeta(3)^2+1/90*(960 *Pi^2+2880*ln(n)+2880*gamma-17760)*Pi^4-11520*Zeta(5), (-30532750703/81000+ 1607347/54*Pi^2-2660/3*Pi^4+(1265600/9-15680*Pi^2+2240/3*Pi^4)*Zeta(3)+1/90*( 63840-53760*Zeta(3))*Pi^4+(-10752*Pi^2+112896)*Zeta(5)+92160*Zeta(7))*n^7+(-\ 258911262071/81000+1607347/18*ln(n)+1607347/18*gamma+1/6*(14118139/9-31920*ln(n )-31920*gamma)*Pi^2-27860/3*Pi^4+264*Pi^6+(9779840/9-47040*ln(n)-47040*gamma+1/ 6*(-645120+26880*ln(n)+26880*gamma)*Pi^2+15680/3*Pi^4)*Zeta(3)-53760*Zeta(3)^2+ 1/90*(668640-20160*Pi^2-376320*Zeta(3))*Pi^4+(-75264*Pi^2-32256*ln(n)-32256* gamma+774144)*Zeta(5)+645120*Zeta(7))*n^6+(-236914984117/20250+6888196/9*ln(n)+ 6888196/9*gamma-7980*(ln(n)+gamma)^2+1/6*(52022012/9-349440*ln(n)-349440*gamma) *Pi^2+1/36*(-1323840+43680*ln(n)+43680*gamma)*Pi^4+1584*Pi^6+(34672960/9-275520 *ln(n)-275520*gamma+6720*(ln(n)+gamma)^2+1/6*(-2038400+161280*ln(n)+161280* gamma)*Pi^2+15680*Pi^4)*Zeta(3)-322560*Zeta(3)^2+1/90*(2647680-87360*ln(n)-\ 87360*gamma-120960*Pi^2-1128960*Zeta(3))*Pi^4+(-225792*Pi^2-193536*ln(n)-193536 *gamma+2446080)*Zeta(5)+1935360*Zeta(7))*n^5+(-65504190101/2700+2627030*ln(n)+ 2627030*gamma-91140*(ln(n)+gamma)^2+1/6*(35870170/3-1249920*ln(n)-1249920*gamma +28560*(ln(n)+gamma)^2)*Pi^2+1/36*(-2795520+218400*ln(n)+218400*gamma)*Pi^4+ 3960*Pi^6+(7871360-822080*ln(n)-822080*gamma+33600*(ln(n)+gamma)^2+1/6*(-\ 3808000+403200*ln(n)+403200*gamma)*Pi^2+78400/3*Pi^4)*Zeta(3)-806400*Zeta(3)^2+ 1/90*(5591040-436800*ln(n)-436800*gamma-302400*Pi^2-1881600*Zeta(3))*Pi^4+(-\ 376320*Pi^2-483840*ln(n)-483840*gamma+4569600)*Zeta(5)+3225600*Zeta(7))*n^4+(-\ 2497849117127/81000+45885581/9*ln(n)+45885581/9*gamma-278460*(ln(n)+gamma)^2+ 5880*(ln(n)+gamma)^3+1/6*(136419283/9-2370928*ln(n)-2370928*gamma+114240*(ln(n) +gamma)^2)*Pi^2+1/36*(-3512880+436800*ln(n)+436800*gamma)*Pi^4+5280*Pi^6+( 88608464/9-1473920*ln(n)-1473920*gamma+67200*(ln(n)+gamma)^2+1/6*(-4457600+ 537600*ln(n)+537600*gamma)*Pi^2+78400/3*Pi^4)*Zeta(3)-1075200*Zeta(3)^2+1/90*( 7025760-873600*ln(n)-873600*gamma-403200*Pi^2-1881600*Zeta(3))*Pi^4+(-376320*Pi ^2-645120*ln(n)-645120*gamma+5349120)*Zeta(5)+3225600*Zeta(7))*n^3+(-\ 1929920135899/81000+104906753/18*ln(n)+104906753/18*gamma-489244*(ln(n)+gamma)^ 2+17640*(ln(n)+gamma)^3+1/6*(104460755/9-2628864*ln(n)-2628864*gamma+171360*(ln (n)+gamma)^2)*Pi^2+1/36*(-2659440+436800*ln(n)+436800*gamma)*Pi^4+3960*Pi^6+( 67381552/9-1538880*ln(n)-1538880*gamma+67200*(ln(n)+gamma)^2+1/6*(-3207680+ 403200*ln(n)+403200*gamma)*Pi^2+15680*Pi^4)*Zeta(3)-806400*Zeta(3)^2+1/90*( 5318880-873600*ln(n)-873600*gamma-302400*Pi^2-1128960*Zeta(3))*Pi^4+(-225792*Pi ^2-483840*ln(n)-483840*gamma+3849216)*Zeta(5)+1935360*Zeta(7))*n^2+(-\ 418854185351/40500+3765029*ln(n)+3765029*gamma-467768*(ln(n)+gamma)^2+17640*(ln (n)+gamma)^3+1/6*(43453046/9-1588944*ln(n)-1588944*gamma+114240*(ln(n)+gamma)^2 )*Pi^2+1/36*(-1125600+218400*ln(n)+218400*gamma)*Pi^4+1584*Pi^6+(28761712/9-\ 848960*ln(n)-848960*gamma+33600*(ln(n)+gamma)^2+1/6*(-1294720+161280*ln(n)+ 161280*gamma)*Pi^2+15680/3*Pi^4)*Zeta(3)-322560*Zeta(3)^2+1/90*(2251200-436800* ln(n)-436800*gamma-120960*Pi^2-376320*Zeta(3))*Pi^4+(-75264*Pi^2-193536*ln(n)-\ 193536*gamma+1553664)*Zeta(5)+645120*Zeta(7))*n+1084302*ln(n)+1084302*gamma-\ 173824*(ln(n)+gamma)^2+5880*(ln(n)+gamma)^3+1/6*(28560*(ln(n)+gamma)^2-398608* ln(n)-398608*gamma+812476)*Pi^2+1/36*(-204960+43680*ln(n)+43680*gamma)*Pi^4+264 *Pi^6+(589456-190400*ln(n)-190400*gamma+6720*(ln(n)+gamma)^2+1/6*(-224000+26880 *ln(n)+26880*gamma)*Pi^2+2240/3*Pi^4)*Zeta(3)-53760*Zeta(3)^2+1/90*(409920-\ 87360*ln(n)-87360*gamma-20160*Pi^2-53760*Zeta(3))*Pi^4+(-10752*Pi^2-32256*ln(n) -32256*gamma+268800)*Zeta(5)+92160*Zeta(7), (90558126238639/14883750-1039507238 /2025*Pi^2+632800/27*Pi^4-7840/9*Pi^6-10256/135*Pi^8+(-51435104/27+340480/3*Pi^ 2)*Zeta(3)+(501760-143360/3*Pi^2)*Zeta(3)^2+1/90*(-5062400/3+188160*Pi^2-8960* Pi^4)*Pi^4+(-817152+688128*Zeta(3))*Zeta(5)+1/945*(143360*Pi^2-1505280)*Pi^6)*n ^8+(874593379118567/14883750-1039507238/675*ln(n)-1039507238/675*gamma+1/6*(-\ 19781753348/675+2531200/3*ln(n)+2531200/3*gamma)*Pi^2+1/36*(22473920/3-282240* ln(n)-282240*gamma)*Pi^4+1/216*(-1478400+53760*ln(n)+53760*gamma)*Pi^6-82048/ 135*Pi^8+(-518402752/27+340480*ln(n)+340480*gamma+4094720/3*Pi^2-62720/3*Pi^4)* Zeta(3)+(3942400-143360*ln(n)-143360*gamma-1146880/3*Pi^2)*Zeta(3)^2+1/90*(-\ 44947840/3+564480*ln(n)+564480*gamma+1/6*(8870400-322560*ln(n)-322560*gamma)*Pi ^2-71680*Pi^4+1505280*Zeta(3))*Pi^4+(-9827328+301056*Pi^2+5505024*Zeta(3))*Zeta (5)+1/945*(1146880*Pi^2+430080*ln(n)+430080*gamma-11827200)*Pi^6-2580480*Zeta(7 ))*n^7+(179330966527777/708750-3164769412/225*ln(n)-3164769412/225*gamma+632800 /3*(ln(n)+gamma)^2+1/6*(-9444274952/75+20964160/3*ln(n)+20964160/3*gamma-141120 *(ln(n)+gamma)^2)*Pi^2+1/36*(40320*(ln(n)+gamma)^2-1935360*ln(n)-1935360*gamma+ 31231200)*Pi^4+1/216*(-5496960+376320*ln(n)+376320*gamma)*Pi^6-287168/135*Pi^8+ (-249141088/3+4256000*ln(n)+4256000*gamma+1/6*(37954560-1039360*ln(n)-1039360* gamma)*Pi^2-439040/3*Pi^4)*Zeta(3)+(14658560-1003520*ln(n)-1003520*gamma-\ 4014080/3*Pi^2)*Zeta(3)^2+1/90*(-62462400+3870720*ln(n)+3870720*gamma-80640*(ln (n)+gamma)^2+1/6*(32981760-2257920*ln(n)-2257920*gamma)*Pi^2-250880*Pi^4+ 10536960*Zeta(3))*Pi^4+(-45545472+1247232*ln(n)+1247232*gamma+2107392*Pi^2+ 19267584*Zeta(3))*Zeta(5)+1/945*(4014080*Pi^2+3010560*ln(n)+3010560*gamma-\ 43975680)*Pi^6-18063360*Zeta(7))*n^6+(1349840076770897/2126250-39364084648/675* ln(n)-39364084648/675*gamma+1621200*(ln(n)+gamma)^2-23520*(ln(n)+gamma)^3+1/6*( -212857318856/675+85544480/3*ln(n)+85544480/3*gamma-826560*(ln(n)+gamma)^2+ 13440*(ln(n)+gamma)^3)*Pi^2+1/36*(231462560/3-6834240*ln(n)-6834240*gamma+ 241920*(ln(n)+gamma)^2)*Pi^4+1/216*(-12472320+1128960*ln(n)+1128960*gamma)*Pi^6 -574336/135*Pi^8+(-5621507584/27+18161920*ln(n)+18161920*gamma-331520*(ln(n)+ gamma)^2+1/6*(96992000-6236160*ln(n)-6236160*gamma)*Pi^2-439040*Pi^4)*Zeta(3)+( 33259520-3010560*ln(n)-3010560*gamma-8028160/3*Pi^2)*Zeta(3)^2+1/90*(-462925120 /3+13668480*ln(n)+13668480*gamma-483840*(ln(n)+gamma)^2+1/6*(74833920-6773760* ln(n)-6773760*gamma)*Pi^2-501760*Pi^4+31610880*Zeta(3))*Pi^4+(-116390400+ 7483392*ln(n)+7483392*gamma+6322176*Pi^2+38535168*Zeta(3))*Zeta(5)+1/945*( 8028160*Pi^2+9031680*ln(n)+9031680*gamma-99778560)*Pi^6-54190080*Zeta(7))*n^5+( 1087322442362819/1063125-18614211196/135*ln(n)-18614211196/135*gamma+19847240/3 *(ln(n)+gamma)^2-114240*(ln(n)+gamma)^3+1680*(ln(n)+gamma)^4+1/6*(-341742271444 /675+66893120*ln(n)+66893120*gamma-2924320*(ln(n)+gamma)^2+67200*(ln(n)+gamma)^ 3)*Pi^2+1/36*(366738064/3-15019200*ln(n)-15019200*gamma+604800*(ln(n)+gamma)^2) *Pi^4+1/216*(-18480000+1881600*ln(n)+1881600*gamma)*Pi^6-143584/27*Pi^8+(-\ 9013029536/27+42521472*ln(n)+42521472*gamma-1657600*(ln(n)+gamma)^2+1/6*( 154604800-15590400*ln(n)-15590400*gamma)*Pi^2-2195200/3*Pi^4)*Zeta(3)+(49280000 -5017600*ln(n)-5017600*gamma-10035200/3*Pi^2)*Zeta(3)^2+1/90*(-733476128/3+ 30038400*ln(n)+30038400*gamma-1209600*(ln(n)+gamma)^2+1/6*(110880000-11289600* ln(n)-11289600*gamma)*Pi^2-627200*Pi^4+52684800*Zeta(3))*Pi^4+(-185525760+ 18708480*ln(n)+18708480*gamma+10536960*Pi^2+48168960*Zeta(3))*Zeta(5)+1/945*( 10035200*Pi^2+15052800*ln(n)+15052800*gamma-147840000)*Pi^6-90316800*Zeta(7))*n ^4+(385806806670149/354375-15542468438/75*ln(n)-15542468438/75*gamma+42892360/3 *(ln(n)+gamma)^2-440720*(ln(n)+gamma)^3+6720*(ln(n)+gamma)^4+1/6*(-13429314276/ 25+294611632/3*ln(n)+294611632/3*gamma-6254080*(ln(n)+gamma)^2+134400*(ln(n)+ gamma)^3)*Pi^2+1/36*(806400*(ln(n)+gamma)^2-20563200*ln(n)-20563200*gamma+ 127119552)*Pi^4+1/216*(-17928960+1881600*ln(n)+1881600*gamma)*Pi^6-574336/135* Pi^8+(-350956704+61669888*ln(n)+61669888*gamma-3315200*(ln(n)+gamma)^2+1/6*( 159093760-20787200*ln(n)-20787200*gamma)*Pi^2-2195200/3*Pi^4)*Zeta(3)+(47810560 -5017600*ln(n)-5017600*gamma-8028160/3*Pi^2)*Zeta(3)^2+1/90*(-254239104+ 41126400*ln(n)+41126400*gamma-1612800*(ln(n)+gamma)^2+1/6*(107573760-11289600* ln(n)-11289600*gamma)*Pi^2-501760*Pi^4+52684800*Zeta(3))*Pi^4+(-190912512+ 24944640*ln(n)+24944640*gamma+10536960*Pi^2+38535168*Zeta(3))*Zeta(5)+1/945*( 8028160*Pi^2+15052800*ln(n)+15052800*gamma-143431680)*Pi^6-90316800*Zeta(7))*n^ 3+(5541994352458664/7441875-134052429784/675*ln(n)-134052429784/675*gamma+ 19398596*(ln(n)+gamma)^2-871920*(ln(n)+gamma)^3+10080*(ln(n)+gamma)^4+1/6*(-\ 245764976812/675+273896336/3*ln(n)+273896336/3*gamma-7365120*(ln(n)+gamma)^2+ 134400*(ln(n)+gamma)^3)*Pi^2+1/36*(253947904/3-16813440*ln(n)-16813440*gamma+ 604800*(ln(n)+gamma)^2)*Pi^4+1/216*(-10953600+1128960*ln(n)+1128960*gamma)*Pi^6 -287168/135*Pi^8+(-6376619648/27+54810112*ln(n)+54810112*gamma-3315200*(ln(n)+ gamma)^2+1/6*(103165440-15590400*ln(n)-15590400*gamma)*Pi^2-439040*Pi^4)*Zeta(3 )+(29209600-3010560*ln(n)-3010560*gamma-4014080/3*Pi^2)*Zeta(3)^2+1/90*(-\ 507895808/3+33626880*ln(n)+33626880*gamma-1209600*(ln(n)+gamma)^2+1/6*(65721600 -6773760*ln(n)-6773760*gamma)*Pi^2-250880*Pi^4+31610880*Zeta(3))*Pi^4+(-\ 123798528+18708480*ln(n)+18708480*gamma+6322176*Pi^2+19267584*Zeta(3))*Zeta(5)+ 1/945*(4014080*Pi^2+9031680*ln(n)+9031680*gamma-87628800)*Pi^6-54190080*Zeta(7) )*n^2+(2220764432107573/7441875-25625106974/225*ln(n)-25625106974/225*gamma+ 46582256/3*(ln(n)+gamma)^2-761040*(ln(n)+gamma)^3+6720*(ln(n)+gamma)^4+1/6*(-\ 94588678544/675+147019376/3*ln(n)+147019376/3*gamma-4379200*(ln(n)+gamma)^2+ 67200*(ln(n)+gamma)^3)*Pi^2+1/36*(98553056/3-7479360*ln(n)-7479360*gamma+241920 *(ln(n)+gamma)^2)*Pi^4+1/216*(-3816960+376320*ln(n)+376320*gamma)*Pi^6-82048/ 135*Pi^8+(-2506606816/27+27039488*ln(n)+27039488*gamma-1657600*(ln(n)+gamma)^2+ 1/6*(38357760-6236160*ln(n)-6236160*gamma)*Pi^2-439040/3*Pi^4)*Zeta(3)+( 10178560-1003520*ln(n)-1003520*gamma-1146880/3*Pi^2)*Zeta(3)^2+1/90*(-197106112 /3+14958720*ln(n)+14958720*gamma-483840*(ln(n)+gamma)^2+1/6*(22901760-2257920* ln(n)-2257920*gamma)*Pi^2-71680*Pi^4+10536960*Zeta(3))*Pi^4+(-46029312+7483392* ln(n)+7483392*gamma+2107392*Pi^2+5505024*Zeta(3))*Zeta(5)+1/945*(1146880*Pi^2+ 3010560*ln(n)+3010560*gamma-30535680)*Pi^6-18063360*Zeta(7))*n-30434570*ln(n)-\ 30434570*gamma+5220796*(ln(n)+gamma)^2-239120*(ln(n)+gamma)^3+1680*(ln(n)+gamma )^4+1/6*(13440*(ln(n)+gamma)^3-1029280*(ln(n)+gamma)^2+11388944*ln(n)+11388944* gamma-22569628)*Pi^2+1/36*(40320*(ln(n)+gamma)^2-1391040*ln(n)-1391040*gamma+ 5645808)*Pi^4+1/216*(-577920+53760*ln(n)+53760*gamma)*Pi^6-10256/135*Pi^8+(-\ 16259040+5624192*ln(n)+5624192*gamma-331520*(ln(n)+gamma)^2+1/6*(6227200-\ 1039360*ln(n)-1039360*gamma)*Pi^2-62720/3*Pi^4)*Zeta(3)+(1541120-143360*ln(n)-\ 143360*gamma-143360/3*Pi^2)*Zeta(3)^2+1/90*(-11291616+2782080*ln(n)+2782080* gamma-80640*(ln(n)+gamma)^2+1/6*(3467520-322560*ln(n)-322560*gamma)*Pi^2-8960* Pi^4+1505280*Zeta(3))*Pi^4+(-7472640+1247232*ln(n)+1247232*gamma+301056*Pi^2+ 688128*Zeta(3))*Zeta(5)+1/945*(143360*Pi^2+430080*ln(n)+430080*gamma-4623360)* Pi^6-2580480*Zeta(7)] The limit of the scaled moments, from the 3rd to the, 8, -th is 2 4 -19 + 16 Zeta(3) 2260/9 - 28 Pi + 4/15 Pi [----------------, --------------------------, / 2\3/2 / 2\2 | 2 Pi | | 2 Pi | |7 - -----| |7 - -----| \ 3 / \ 3 / 2 / 2\ 229621 380 Pi | 320 Pi | - ------ + ------- + |1120 - -------| Zeta(3) + 768 Zeta(5) / 108 3 \ 3 / |74250517 -----------------------------------------------------------, |-------- / 2\5/2 \ 2700 | 2 Pi | |7 - -----| \ 3 / 2 6 22600 Pi 4 88 Pi 2 - --------- + 140 Pi - ------ - 6080 Zeta(3) + 2560 Zeta(3) 9 7 2 4\ / 2\3 / 2 (960 Pi - 10080) Pi | / | 2 Pi | | 30532750703 1607347 Pi + ---------------------| / |7 - -----| , |- ----------- + ----------- 90 / / \ 3 / \ 81000 54 4 2660 Pi 2 4 - -------- + (1265600/9 - 15680 Pi + 2240/3 Pi ) Zeta(3) 3 4 2 + 1/90 (63840 - 53760 Zeta(3)) Pi + (-10752 Pi + 112896) Zeta(5) \ / 2\7/2 / 2 | / | 2 Pi | |90558126238639 1039507238 Pi + 92160 Zeta(7)| / |7 - -----| , |-------------- - -------------- / / \ 3 / \ 14883750 2025 4 6 8 / 2\ 632800 Pi 7840 Pi 10256 Pi | 51435104 340480 Pi | + ---------- - -------- - --------- + |- -------- + ----------| Zeta(3) 27 9 135 \ 27 3 / / 2\ | 143360 Pi | 2 + |501760 - ----------| Zeta(3) \ 3 / 2 4 4 (- 5062400/3 + 188160 Pi - 8960 Pi ) Pi + ----------------------------------------- 90 2 6\ (143360 Pi - 1505280) Pi | / + (-817152 + 688128 Zeta(3)) Zeta(5) + --------------------------| / 945 / / / 2\4 | 2 Pi | |7 - -----| ] \ 3 / and in Maple format [(-19+16*Zeta(3))/(7-2/3*Pi^2)^(3/2), (2260/9-28*Pi^2+4/15*Pi^4)/(7-2/3*Pi^2)^2 , (-229621/108+380/3*Pi^2+(1120-320/3*Pi^2)*Zeta(3)+768*Zeta(5))/(7-2/3*Pi^2)^( 5/2), (74250517/2700-22600/9*Pi^2+140*Pi^4-88/7*Pi^6-6080*Zeta(3)+2560*Zeta(3)^ 2+1/90*(960*Pi^2-10080)*Pi^4)/(7-2/3*Pi^2)^3, (-30532750703/81000+1607347/54*Pi ^2-2660/3*Pi^4+(1265600/9-15680*Pi^2+2240/3*Pi^4)*Zeta(3)+1/90*(63840-53760* Zeta(3))*Pi^4+(-10752*Pi^2+112896)*Zeta(5)+92160*Zeta(7))/(7-2/3*Pi^2)^(7/2), ( 90558126238639/14883750-1039507238/2025*Pi^2+632800/27*Pi^4-7840/9*Pi^6-10256/ 135*Pi^8+(-51435104/27+340480/3*Pi^2)*Zeta(3)+(501760-143360/3*Pi^2)*Zeta(3)^2+ 1/90*(-5062400/3+188160*Pi^2-8960*Pi^4)*Pi^4+(-817152+688128*Zeta(3))*Zeta(5)+1 /945*(143360*Pi^2-1505280)*Pi^6)/(7-2/3*Pi^2)^4] In floating-point this is [.85488186713258853660, 4.1781156382698542397, 10.646163374673878503, 44.427077\ 708169777614, 179.72191973561786840, 858.20320399000226017] --------------------- This took, 158.568, seconds.