Help:=proc(): print(`Zetap(s,N), Zetas(s,N), `): print(` ACzeta(s,N) `): end: #The product of 1/(1-1/p^s) for the first N primes #in floating point, and s a complex number (in floating) Zetap:=proc(s,N) local x,i: evalf(mul(1./(1-1/ithprime(i)^s),i=1..N)): end: #The sum of 1/n^s for n from 1 to N #in floating point, and s a complex number (in floating) Zetas:=proc(s,N) local n: evalf(add(1/n^s,n=1..N)): end: #ACzeta(s,N): zeta(s)-1/(s-1) using the first line of #page 3 in Don Zagier's paper ACzeta:=proc(s,N) local x,n: evalf(add(int(1/n^s-1/x^s,x=n..n+1) , n=1..N)): end: