In this paper, we obtain a (p, ν)-extension of Srivastava’s triple hypergeometric function HB (⋅), by using the extended beta function Bp,ν (x, y) introduced in [R. K. Parmar, P. Chopra and R. B. Paris, On an extension of extended beta and hypergeometric functions, J. Class. Anal. 11 (2017), no. 2, 91–106]. We give some of the main properties of this extended function, which include several integral representations involving Exton’s hypergeometric function, the Mellin transform, a differential formula, recursion formulas and a bounded inequality.
- Srivastava's triple hypergeometric functions
- Beta and gamma functions
- Exton's triple hypergeometric function
- Bessel function
- Bounded inequality