
Re: Bug in infinite sum
Posted:
Jul 22, 2012 4:33 AM


Am 21.07.2012 05:44, schrieb Dr. Wolfgang Hintze: > Consider this nice sum > > s[x_] = Sum[Binomial[x, k], {k, 0, Infinity}] > 2^x > > and that, (with the odd terms only) > > u[x_] = Sum[Binomial[x, 2*k + 1], {k, 0, Infinity}] > 2^(1 + x) > > But now the even terms only ... and the surprise: > g[x_] = Sum[Binomial[x, 2*k], {k, 0, Infinity}] > > (Sqrt[Pi]*Gamma[1 + x]*GegenbauerC[x, 1/2  x, 1])/ > (2^x*Gamma[1/2 + x]) > > looks complicated, but let's see > FullSimplify[g[x], x > 0] > > 2^x*Cos[Pi*x] > > much simpler, but definitely wrong (giving e.g. 0 for x=1/2) > Of course g should be s  u = 2^x 1/2 2^s = 1/2 2^s. > > Best regards, > Wolfgang >
Hmm on version 8 (Windows 64bit) I get:
Sum[Binomial[x, 2*k], {k, 0, Infinity}] 2^(1+x)
and the same result for
Sum[Binomial[x, k], {k, 0, Infinity, 2}]
as it should be.
Peter

