Appell, P. Sur les fonctions hypergéométriques de plusieurs variables. Paris: Gauthier-Villars, 1925.Appell, P.
and Kampé de Fériet, J. Fonctions hypergéométriques
et hypersphériques: polynomes d'Hermite. Paris: Gauthier-Villars, 1926.Exton,
H. "The Kampé de Fériet Function." §1.3.2 in Handbook
of Hypergeometric Integrals: Theory, Applications, Tables, Computer Programs.
Chichester, England: Ellis Horwood, pp. 24-25, 1978.Exton, H. Multiple
Hypergeometric Functions and Applications. Chichester, England: Ellis Horwood,
1976.Exton, H. and Krupnikov, E. D. A Register of Computer-Oriented
Reduction Identities for the Kampé de Fériet Function. Draft manuscript.
Novosibirsk, 1998.Kampé de Fériet, J. La fonction hypergéométrique.
Paris: Gauthier-Villars, 1937.Ragab, F. J. "Expansions of
Kampe De Feriet's Double Hypergeometric Function of Higher Order." J. reine
angew. Math.212, 113-119, 1963.Srivastava, H. M., Karlsson,
P. W. Multiple
Gaussian Hypergeometric Series. Chichester, England: Ellis Horwood, 1985.
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 (1998) have derived a large collection of formulas involving
this function.
and 
,
where 
is the incomplete elliptic integral
of the second kind and 
is the incomplete elliptic
integral of the first kind, as well as
,
where 
is the incomplete elliptic integral
of the third kind (Exton and Krupnikov 1998, p. 1). Additional identities
are given by
