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

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 ear- lier results. Here, by simply splitting Srivastava s hypergeometric function HB into eight parts, we show how some useful and gener- alized relations between Srivastava s hypergeometric functions HB and F(3) can be obtained. These main results are shown to be spe- cialized to yield certain relations between functions 0F1, 1F1, 0F3,ª2, and their products including di？？erent combinations with dif- ferent values of parameters and signs of variables. We also consider some other interesting relations between the Humbert ª2 function and Kamp¶e de F¶eriet function, and between the product of expo- nential and Bessel functions with Kamp¶e de F¶eriet functions.