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.