In this paper we have solved a double convolution integral equation whose kernel involves the product of theH-functions of several variables and a general class of multivariable polynomials. Due to general nature of the kernel, we can obtain from it, solutions of a large number of double and single convolution integral equations involving products of several classical orthogonal polynomials and simpler functions. We have also obtained here solutions of two double convolution integral equations as special cases of our main result. Exact reference of three known results, which are obtainable as particular cases of one of these special cases, have also been included.

Double convolution integral equations involving a general class of multivariable polynomials and the multivariableH-functions

Recently Srivastava et al.[17, 20], and several others have obtained several results for fractional integral operators in one and more dimensions. Motivated by this, we establish here various theorems involving compositions, inversion formulas, and multidimensional Mellin transforms and convolutions of two new families of multidimensional fractional integral operators involving a generalized polynomial set. Each of the results obtained in this paper would unify and extend the corresponding (known or new) results for simpler families of fractional integral operators.

Multidimensional Fractional Integral Operators Involving a Generalized Polynomial Set

In the present paper we obtain three new and interesting composition formulae of a class of multidimensional fractional integral operators involving the product of the generalized polynomials and the multivariable H-function. On account of the most general nature of the functions used here as kernels, the main results of our paper are unified in nature and capable of yielding a very large number of corresponding results (new and known) involving simpler special functions and polynomials (of one or more variables) as special cases of our formulae. We give here exact references of the five results obtained by [1], Goyal and Jain [10], Gupta and Jain [9], Goyal et al.[11], Srivastava et al.[5] which follow as special case of our findings. Thus the present study unifies and extends a number of composition formulae lying scattered in the literature.

On Composition of Multidimensional Integral Operators Involving General Polynomials and a Multivariable H-Function

In this paper we first solve a convolution integral equation involving product of the general class of polynomials and theH-function of several variables. Due to general nature of the general class of polynomials and theH-function of several variables which occur as kernels in our main convolution integral equation, we can obtain from it solutions of a large number of convolution integral equations involving products of several useful polynomials and special functions as its special cases. We record here only one such special case which involves the product of general class of polynomials and Appell's functionF 3. We also give exact references of two results recently obtained by Srivastavaet al [10] and Rashmi Jain [3] which follow as special cases of our main result.

Pawan Agrawal

Papers

On Composition of Multidimensional Integral Operators Involving General Polynomials and a Multivariable H-Function

Convolution integral equations involving a general class of polynomials and the multivariableH-function