On certain formulas for the multivariable hypergeometric functions. (English) Zbl 0935.33003

Raina, R. K.

Acta Math. Univ. Comen., New Ser. 64, No. 1, 47-56 (1995).

Summary: We present relatively simple and direct proofs of the integral representations established recently by M Saigo and Kim Tuan Vu [Rend. Circ. Mat. Palermo, II. Ser. 41, No. 1, 69-80 (1992; Zbl 0752.33006)]. 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 the paper cited above. Also, an operational formula involving fractional calculus operators for an analytic function is derived and its usefulness illustrated by considering some examples.

MSC:

33C20	Generalized hypergeometric series, \({}_pF_q\)
33C50	Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable
33C60	Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
26A33	Fractional derivatives and integrals

Keywords:

Kampé de Fériet function; \(G\)-function; \(H\)-function; Lauricella function; Gauss function; Riemann-Liouville operator; Erdélyi-Kober operator; fractional calculus operator

Citations:

Zbl 0752.33006