FUNCTIONAL RELATIONS INVOLVING SRIVASTAVA'S HYPERGEOMETRIC FUNCTIONS HB AND F (3)

Abstract

B. C. Carlson [Some extensions of Lardner's relations between 0F3 and Bessel functions, SIAM J. Math. Anal. 1(2) (1970), 232-242] presented several useful relations between Bessel and generalized hypergeometric functions that generalize some earlier results. Here, by simply splitting Srivastava's hypergeometric function HB into eight parts, we show how some useful and generalized relations between Srivastava's hypergeometric functions HB and F (3) can be obtained. These main results are shown to be specialized to yield certain relations between functions 0F1, 1F1, 0F3, Ψ2, and their products including different combinations with different values of parameters and signs of variables. We also consider some other interesting relations between the Humbert Ψ2 function and Kamp´e de F´eriet function, and between the product of exponential and Bessel functions with Kamp´e de F´eriet functions.

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