Re: Simplifying a sum of products of Gamma functions

On Fri, 7 Nov 2003 [EMAIL PROTECTED] wrote:
> I set myself a trap in mathematics that I don't know how to get out of.
>
> I have to simplify away the k factors in the following sum:
> g(x,y)=Sigma over k[(Rho^(k) *Gamma(k+1,x)*Gamma(k,y))/Gamma(k)^2]
> where k goes from 0 to infinite.
>
What's rho, gamma(n,x) and gamma(n) ?
A real constant, an arbitrary real function of two variables and
        an arbitrary real function of one variable?

> Nico Temme greatly helped by giving me a sum of integrals without reference
> to k  for the following case:
>
What integrals? You want the sum to be expressed as a single expression
without an infinite sum?

> f(x,y)=Sigma over k[(Rho^k *Gamma(k,x)Gamma(k,y))/Gamma(k)^2]
> where k goes from 0 to infinite
> I also face the same problem again with:
>
> h(x,y)=Sigma over k[(Rho^k *Gamma(k+1,x)Gamma(k+1,y))/Gamma(k)^2]
> where k varies from 0 to infinite
>
> Any help would be greatly appreciated.
>