Re: hypergeometric GF



carlos@xxxxxxxxxxxx wrote:
> What is the generating function satisfying
>
> a(1)=1/(2*m-1);
> a(n+1) = -(2*m-2+n)*n/(2*(2*m-1+2*n)*(1+n)) * a(n), n>=1
>
> m,n positive integers?

In[65]:= InputForm[a[n] /. First[RSolve[{a[1]==1/(2*m-1),
a[n+1] == -(2*m-2+n)*n/(2*(2*m-1+2*n)*(1+n)) * a[n]}, a[n], n]]]

Out[65]//InputForm=
-(((-1)^n*4^(1 - n)*Gamma[1/2 + m]*Gamma[-2 + 2*m + n])/
((-1 + 2*m)*n*Gamma[-1 + 2*m]*Gamma[-1/2 + m + n]))


Daniel Lichtblau
Wolfram Research

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