Some Integral Results Associated with Generalized Hypergeometric Function

Classical Orthogonal Polynomials ◽

Different Types ◽

In previous papers, it has been introduced a generalized hypergeometric function of two variables. The present paper aims at to derive different types of integral representations for the generalized hypergeometric function. The results derived here are very general in nature and are interesting and can obtain some known and new integrals for various polynomials. Each result is followed by its applications to the classical orthogonal polynomials.

Further Extension of the Generalized Hurwitz-Lerch Zeta Function of Two Variables

Mathematics ◽

10.3390/math7010048 ◽

2019 ◽

Vol 7 (1) ◽

pp. 48

Author(s):

Kottakkaran Sooppy Nisar

Keyword(s):

Zeta Function ◽

Hypergeometric Function ◽

Summation Formula ◽

Integral Representations ◽

Special Cases ◽

Lerch Zeta Function ◽

The main aim of this paper is to provide a new generalization of Hurwitz-Lerch Zeta function of two variables. We also investigate several interesting properties such as integral representations, summation formula, and a connection with the generalized hypergeometric function. To strengthen the main results we also consider some important special cases.

Convolution Integral Equation Involving Generalized Hypergeometric Function and H-function of Two Variables

Journal of Computer and Mathematical Sciences ◽

10.29055/jcms/1080 ◽

2019 ◽

Vol 10 (4) ◽

pp. 954-960

Author(s):

Poonam Kumari ◽

Yashwant Singh

Keyword(s):

Integral Equation ◽

Hypergeometric Function ◽

Convolution Integral ◽

Convolution Integral Equation ◽

Integral representations of generalized Lauricella hypergeometric functions

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171292000863 ◽

1992 ◽

Vol 15 (4) ◽

pp. 653-657 ◽

Cited By ~ 1

Author(s):

Vu Kim Tuan ◽

R. G. Buschman

Keyword(s):

Integral Representation ◽

Hypergeometric Function ◽

Hypergeometric Functions ◽

Integral Representations ◽

Appell Function

The generalized hypergeometric function was introduced by Srivastava and Daoust. In the present paper a new integral representation is derived. Similarly new integral representations of Lauricella and Appell function are obtained.

A new expansion formula for hypergeometric functions of two variables

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100042973 ◽

1968 ◽

Vol 64 (2) ◽

pp. 413-416

Author(s):

B. L. Sharma

Keyword(s):

Hypergeometric Function ◽

Hypergeometric Functions ◽

Expansion Formula ◽

Generalized Hypergeometric Functions ◽

Functions Of Two Variables ◽

The main object of this paper is to derive an expansion formula for a generalized hypergeometric function of two variables in a series of products of generalized hypergeometric functions of two variables and a Meijer's G-function. The result established in this paper is the extension of the results recently given by Srivastava (5) and Verma (6). It is interesting to note that some interesting expansions can be derived from the result by specializing the parameters.

A procedure for deriving inversion formulae for integral transform pairs of a general kind

Glasgow Mathematical Journal ◽

10.1017/s001708950000029x ◽

1968 ◽

Vol 9 (1) ◽

pp. 67-77 ◽

Cited By ~ 8

Author(s):

Ian N. Sneddon

Keyword(s):

Orthogonal Polynomials ◽

Hypergeometric Function ◽

Integral Equations ◽

Integral Transform ◽

Classical Orthogonal Polynomials ◽

General Kind ◽

Image Position

In recent years there have appeared solutions of several integral equations of the typein which the kernel K(x) contains (as a factor) one of the classical orthogonal polynomials or a hypergeometric function.