ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 64,   1   (1995)
pp.   47-56

ON CERTAIN FORMULAS FOR THE MULTIVARIABLE HYPERGEOMETRIC FUNCTIONS
R. K. RAINA


Abstract.  We present relatively simple and direct proofs of the integral representations established recently in Ref. 7. An algorithm is then furnished and applied to obtain new classes of integral formulas for the multivariable hypergeometric functions, thereby, providing generalizations to the results of Ref. 7. Also, an operational formula involving fractional calculus operators for an analytic function is derived and its usefulness illustrated by considering some examples.

AMS subject classification
Keywords.  Kampe de Feriet function, hypergeometric function, $G$ and\break $H$-functions, Lauricella functions, Gauss function, Riemann-Liouville operator, Erdelyi-Kober operator, fractional calculus operator

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