Abstract
The behavior of Lauricella hypergeometric seriesF M andF G (see [2]) near the boundary points of their domains of convergence is discussed. Such properties for one variable series, the Gauss2 F 1 and the Clausen3 F 2, and for two variables, the AppellF 1,F 2 andF 3, are established by the author [5], [7] and the results are effectively applied to solve problems for the Euler-Darboux equation and to calculate multiplications of the fractional calculus operators in the articles by the author [4], [6] and by H. M. Srivastava and the author [9].
Similar content being viewed by others
References
Appell P., Kampé de Fériet J.,Fonctions Hypergéométriques et Hypersphériques, Polynômes d'Hermite, Gauthier-Villars, Paris, 1926.
Lauricella G.,Sulle funzioni ipergeometriche a più variabili, Rend. Circ. Mat. Palermo,7 (1893), 111–158.
Magnus W., Oberhettinger F., Soni R.P.,Formulas and Theorems for the Special Functions of Mathematical Physics, Springer-Verlag, Berlin, 1966.
Saigo M.,A certain boundary value problem for the Euler-Darboux equation, II, Math. Japon.,25 (1980), 211–220.
Saigo M.,on a property of the Appell hypergeometric function F 1 , Math. Rep. Kyushu Univ.,12 (1980), 63–67.
Saigo M.,A certain boundary value problem for the Euler-Darboux equation, III, Math. Japon.,26 (1981), 103–119.
Saigo M.,On properties of the Appell hypergeometric functions F 2 and F 3 and the generalized Gauss function 3 F 2 , Bull. Central Res. Inst. Fukuoka Univ.,66 (1983), 27–32.
Srivastava H.M., Karlsson P.W.,Multiple Gaussian Hypergeometric Series, Ellis Horwood, Chichester, 1985.
Srivastava H.M., Saigo M.,Multiplication of fractional calculus operators and boundary value problems involving the Euler-Darboux equation, J. Math. Anal. Appl.,121 (1987), 325–369.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Saigo, M. On properties of hypergeometric functions of three variables,F M andF G . Rend. Circ. Mat. Palermo 37, 449–468 (1988). https://doi.org/10.1007/BF02844643
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02844643