Trying to figure out if the double sum $ $ f(x,y)=\sum_{n=0}^{\infty}\sum_{m=n}^{\infty}\dfrac{(a)_n\,(b)_n\,(1)_m}{(a)_m\,(b)_m}\dfrac{x^n\, y^m}{n!\,m!}, \;\; \text{where} \;\; (z)_n=z(z+1)\cdots(z+n-1), $ $ is a special case of the generalized hypergeometric function (of two variables). For instance, the Kampé de Fériet function seems to have a similar form, but it looks like Mathematica doesn’t support this function yet, alas. ItRead more