Simplifying a sum of products of Gamma functions

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