Some Finite Integrals Involving The Product of Srivastavas Polynomials and A Certain $\small{\bar{H}}$-Function with Applications

• Journal title : Kyungpook mathematical journal
• Volume 48, Issue 2,  2008, pp.165-171
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2008.48.2.165
Title & Authors
Some Finite Integrals Involving The Product of Srivastavas Polynomials and A Certain $\small{\bar{H}}$-Function with Applications
Singh, Yashwant; Garg, Atul;

Abstract
The aim of this paper is to evaluate four finite integrals involving the product of Srivastava`s polynomials, a generalized hypergeometric function and $\small{\bar{H}}$-function proposed by Inayat Hussian which contains a certain class of Feynman integrals. At the end, we give an application of our main findings by connecting them with the Riemann-Liouville type of fractional integral operator. The results obtained by us are basic in nature and are likely to find useful applications in several fields notably electric networks, probability theory and statistical mechanics.
Keywords
$\small{\bar{H}}$-function;generalized hypergeometric function;general class of polynomials;freactional integral operators;
Language
English
Cited by
References
1.
R.G. Buschman and H.M. Srivastava, The H-function associated with a certain class of Feynman integrals, J.Phys. A: Math. Gen., 23 (1990), 4707-4710.

2.
A. et.al. Erdelyi, Tables of Integral Transforms, vol.II, McGraw-Hill, New-York (1954).

3.
K.C. Gupta and R.C. Soni, New properties of a generalization of hypergeometric series associated with feynman integrals,Kyungpook Mathematical Journal, vol.4(1), (2001), 97-104.

4.
A.A. Inayat-Hussian, New properties of hypergeometric series deriable from feynman integrals:I; Transformation and reduction formulae, J.Phys. A:Math.Gen. 20 (1987), 4109-4117.

5.
A.A. Inayat-Hussian, New properties of hypergeometric series deriable from feynman integrals:II; A generalization of the H-function, J.Phys. A:Math.Gen. 20 (1987), 4119-4128.

6.
E.D. Rainville, Special Functions, The Macmillan Company Inc., NewYork (1963).

7.
H.M. Srivastava, A contour integral involving Fox's H-function, Indian J.Math., 14 (1972), 1-6.

8.
H.M. Srivastava, K.C. Gupta and S.P. Goyal, The H-function of One and Two Variables with Application; South Asian Publisher, New Delhi (1982).

9.
H.M. Srivastava and N.P. Singh, The integration of certain products of the multivariable H-function with a general class of polynomials, Rend. Circ. Math.Palermo, (Ser2), 32 (1983), 157-187.