Saalschützian

For a Generalized Hypergeometric Function

$${}_{p+1}F_p\left[{\matrix{\alpha_1, \alpha_2, \ldots, \alpha_{p+1}\cr \beta_1, \beta_2, \ldots, \beta_p\cr} ; z}\right],$$

the Saalschützian $S$ is defined if

$$\sum\beta=\sum\alpha+1.$$

See also Generalized Hypergeometric Function