An Integral Involving the Product of three H Functions

Abstract

The object of this paper is to evaluate an integral involving the product of three H functions. Since the H function is of the most general nature, this integral generalizes many known results. Results recently proved by GUPTA and JAIN [ 8 ] and MALOO [lo, p. 3641 are deduced. Deflnitions and results usedIf then 0 ( p ) is called the LAPLACE transform of f(t) and this relation is denoted by f(t) =+ 0 (PI or 0 ( p ) +f(t). M {f(z)} = J z 8 -I f(z) dz. The I&LLIN transform is defined and denoted by m (1.2) 0 (a), = a ( a + i ) (a + 2) --* (a + n, -1); (a)o = 1.j ( a j , eJn denotes the set of n, pairs of parameters i(aj)lh represents the n parameters a,, a2, . . ., a,.