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. The aim of this paper is to evaluate four nite integrals involving the productof Srivastava’s polynomials, a generalized hypergeometric function and H¯ -function pro-posed by Inayat Hussian which contains a certain class of Feynman integrals. At the end,we give an application of our main ndings by connecting them with the Riemann-Liouvilletype of fractional integral operator. The results obtained by us are basic in nature andare likely to nd useful applications in several elds notably electric networks, probabilitytheory and statistical mechanics. 1. IntroductionThe H¯-function will be dened and represented as follows [1]:(1.1) H¯ M,NP,Q [Z] = H¯P,Q [z| (a j ,α j ;A ) 1,N ,(a ,α ) N+1,P (b j ,β j ) 1,M , j j ;B j ) M+1,Q ] =12πiZ i∞−i∞ φ¯(ξ)z ξ dξ,where(1.2) φ¯(ξ) = MQj=1 Γ(b j −β j ξ) N {Γ(1−a j +α j ξ)} A j Q Pj=N+1 Γ(a j −α j ξ) Qj=M+1 {Γ(1−b j +β j ξ)} B j .Buschman and Srivastava [1] has proved that the integral on the right hand side Received September 15, 2003.2000 Mathematics Subject Classication: 33c60, 26A33.Key words and phrases: H¯ -function, generalized hypergeometric function, general classof polynomials, freactional integral operators.

Some Finite Integrals Involving The Product of Srivastava's Polynomials and A Certain <TEX>$\bar{H}$</TEX>-Function with Applications