Certain Unified Integrals Associated with Product of M-Series and Incomplete H-functions

Manish Kumar Bansal,Kottakkaran Sooppy Nisar,Jagdev Singh,Ilyas Khan,Devendra Kumar

doi:10.3390/math7121191

Abstract

In this paper, we established some interesting integrals associated with the product of M-series and incomplete H-functions, which are expressed in terms of incomplete H-functions. Next, we give some special cases by specializing the parameters of M-series and incomplete H-functions (for example, Fox’s H-Function, Incomplete Fox Wright functions, Fox Wright functions and Incomplete generalized hypergeometric functions) and also listed few known results. The results obtained in this work are general in nature and very useful in science, engineering and finance.

Highlights

In this paper, we established some interesting integrals associated with the product of M-series and incomplete H-functions, which are expressed in terms of incomplete H-functions
The incomplete H-functions Γm,n p,q ( z ) and γ p,q ( z ) in (6) and (7) respectively, exist for all y = 0 under the same set of conditions and the same set of contour stated in the articles presented by Kilbas et al [15], Mathai and Saxena [16] and Mathai et al [17]
We have derived some interesting integrals involving the product of M-series and incomplete H-functions, which are expressed in terms of incomplete H-functions

Summary

Introduction

We established some interesting integrals associated with the product of M-series and incomplete H-functions, which are expressed in terms of incomplete H-functions. The results obtained in this work are general in nature and very useful in science, engineering and finance. The integral formula containing several generalized special functions (GSF) have been explored by numerous authors [1,2,3,4,5]. GSF are connected with different kinds of problems in various fields of mathematical sciences. Several unified integral formulas established by many authors involving a various kind of special functions (see, for example, [6,7,8]). The key aim of this work is to develop Oberhettinger’s integral formulas containing the product of M-series and incomplete H-functions. The Oberhettinger’s integral formulas established in the present work are very useful to obtain the Mellin transform of various simpler special functions.

Objectives

Conclusion