The Kampé de Fériet function is a special function that generalizes the generalized hypergeometric function to two variables and includes the Appell hypergeometric function F_1(α;β, β' ;γ;x, y) as a special case. The Kampé de Fériet function can represent derivatives of generalized hypergeometric functions with respect to their parameters, as well as indefinite integrals of two and three Meijer G-functions. Exton and Krupnikov have derived a large collection of formulas involving this function. Kampé de Fériet functions are written in the notation F_(q, s, u)^(p, r, t)(c_p d_q|a_r b_s|α_t β_u|x, y).

Appell hypergeometric function | Fox H-function | generalized hypergeometric function | Horn function | Lauricella functions | MacRobert's E-function | Meijer G-function