|Bill Allombert on Tue, 06 May 2014 15:21:49 +0200|
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On Tue, May 06, 2014 at 01:41:29AM -0400, Charles Greathouse wrote: > I would like to integrate (the product of 1 - q^n for n >= 1) from q = -1 > to 1. Is there a way to do this in GP? I tried variants of > > eps=2e-19; > intnum(z=-1+eps,1-eps, eta(log(z)/2/Pi/I)) > > but without any luck. Your product is called the Euler function in Wikipedia. It can be computed using one of the functions below: eta1(q)=if(q==0,1,prod(n=1,log(10^-38)/log(abs(q)), 1-q^n,1.)) eta2(q)=if(q==0,1,my(p=log(10^-38)/log(abs(q)),N=floor(sqrt(2*p/3)));sum(n=-N,N,(-1)^n*q^((3*n^2-n)/2),0.)) (the second is faster) So a rough estimation of your integral is ? intnum(q=-.99999,.99999,g(q)) %31 = 1.2883008886739212301815836032595770056 Cheers, Bill.