  In this paper, we obtain a $(p,\nu)$-extension of Srivastava's triple
hypergeometric function $H_B(\cdot)$, together by using the extended Beta
function $B_{p,\nu}(x,y)$ introduced in arXiv:1502.06200. 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.
