# On expressions of hypergeometric functions of two variables

I'm looking for a (confluent) hypergeometric function of two variables that can be expressed in terms of a weighted infinite sum of two Whittaker functions such as: $$\sum_{n=0}^\infty (\text{n-dependent product of Gamma functions})W_{\kappa_1\pm n,\mu}(z)W_{\kappa_2\pm n,\mu}(w)\ ,$$ or $$\sum_{n=0}^\infty (\text{n-dependent product of Gamma functions})W_{\kappa_1\pm n,\mu}(z)W_{\kappa_2\mp n,\mu}(w)\ ,$$ where $$\kappa_1,\kappa_2,\mu$$ are some constant.

Could you give me some examples of the two variable hypergeometric functions expressed in the way I specified above? I would appreciate it if you tell me reference books or papers.