read `CfiniteIntegral.txt`:


print(`Examples of procedure IntCS: `):
print(``):
print(`To test Theorem 1 of Seon-Hong Kim's article:`):
print(` On some integrals involving Chebyshev polynomials", Ramanujan J. v. 38 (2015),`):
print(`(629-639) `):
print(` First part: i.e. Int(U_(2n)(x)*U*x_(2n)(x),x=-1..1).. Try: `):

 H1:=IntCS([[1,2*x],[2*x,-1]],x,2,n,N,(1+(-1)^n)/(n+1),10); 
 evalb(SeqFromRec(H1,n,N,50)=SHK1a(50));

print(``):

print(` Second part: i.e. Int(T_(2n)(x)*Star(T_(2n))(x),x=-1..1).. Try: `):
H2:=IntCS([[1,x],[2*x,-1]],x,2,n,N,(1+(-1)^n)/(n+1),10);

evalb(SeqFromRec(H2,n,N,50)=SHK1b(50));

print(``):
print(`For Theorem 2 of that paper, First part: `):

IntCS([[1,x],[2*x,-1]],x,2,n,N, (1+(-1)^n)/2*binomial(n,n/2)/2^n,10);

print(`Second part:  `):

 IntCS([[1,2*x],[2*x,-1]],x,2,n,N, (1+(-1)^n)/2*binomial(n,n/2)/2^n/(n+2),10);

quit: