Lauricella Functions
Lauricella functions are generalizations of the Gauss hypergeometric functions to multiple variables. Four such generalizations were investigated by Lauricella (1893), and more fully by Appell and Kampé de Fériet (1926, p. 117). Let n be the number of variables, then the Lauricella functions are defined by
If n=2, then these functions reduce to the Appell hypergeometric functions F_2, F_3, F_4, and F_1, respectively. If n=1, all four become the Gauss hypergeometric function _2F_1 (Exton 1978, p. 29).
See also
Appell Hypergeometric Function, Generalized Hypergeometric Function, Horn Function, Kampé de Fériet FunctionThis entry contributed by Ronald M. Aarts
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References
Appell, P. and Kampé de Fériet, J. Fonctions hypergéométriques et hypersphériques: polynomes d'Hermite. Paris, France: Gauthier-Villars, 1926.Erdélyi, A. "Hypergeometric Functions of Two Variables." Acta Math. 83, 131-164, 1950.Exton, H. "The Lauricella Functions and Their Confluent Forms," "Convergence," and "Systems of Partial Differential Equations." §1.4.1-1.4.3 in Handbook of Hypergeometric Integrals: Theory, Applications, Tables, Computer Programs. Chichester, England: Ellis Horwood, pp. 29-31, 1978.Exton, H. Ch. 5 in Multiple Hypergeometric Functions and Applications. New York: Wiley, 1976.Lauricella, G. "Sulla funzioni ipergeometriche a più variabili." Rend. Circ. Math. Palermo 7, 111-158, 1893.Srivastava, H. M. and Karlsson, P. W. Multiple Gaussian Hypergeometric Series. Chichester, England: Ellis Horwood, 1985.Referenced on Wolfram|Alpha
Lauricella FunctionsCite this as:
Aarts, Ronald M. "Lauricella Functions." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/LauricellaFunctions.html