Simplifying a sum of products of Gamma functions

[xbru...@skynet.be]

Hi everybody,

I am writing a scientific paper in logistics.
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.

Nico Temme greatly helped by giving me a sum of integrals without reference
to k for
the following case:
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.

--
Xavier

[William Elliot]

On Fri, 7 Nov 2003 xbru...@skynet.be 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?