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

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

Zbl 0752.33006
Full Text: