Some extended-type hypergeometric functions of two and three variables

Shilpi Jain; Praveen Agarwal

doi:10.1016/B978-0-44-336484-6.00011-4

Some extended-type hypergeometric functions of two and three variables

Shilpi Jain
, Praveen Agarwal

Nonlinear Dynamic Research Centre (NDRC)

Poornima College of Engineering
International College of Engineering

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

The major objective of the present chapter is to study the new extension of hypergeometric functions of two and three variables by using the 2-parameter Mittag-Leffler function. In the present chapter, we mainly study the integral representations of these extended hypergeometric functions and obtain some important properties of the extended Riemann-Liouville-type fractional derivative operator. We have also derived some generating functions for the generalized hypergeometric functions by using the extended Riemann-Liouville-type fractional derivative operator.

Original language	English
Title of host publication	Extended Hypergeometric Functions and Orthogonal Polynomials
Publisher	Elsevier
Pages	31-44
Number of pages	14
ISBN (Electronic)	9780443364846
ISBN (Print)	9780443364853
DOIs	https://doi.org/10.1016/B978-0-44-336484-6.00011-4
State	Published - 1 Jan 2026

Keywords

Appell's hypergeometric functions of two variables and Lauricella's hypergeometric function of three variables
Beta function
Hypergeometric function
Mittag-Leffler function
Riemann-Liouville fractional derivative operator

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10.1016/B978-0-44-336484-6.00011-4

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AB - The major objective of the present chapter is to study the new extension of hypergeometric functions of two and three variables by using the 2-parameter Mittag-Leffler function. In the present chapter, we mainly study the integral representations of these extended hypergeometric functions and obtain some important properties of the extended Riemann-Liouville-type fractional derivative operator. We have also derived some generating functions for the generalized hypergeometric functions by using the extended Riemann-Liouville-type fractional derivative operator.

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KW - Beta function

KW - Hypergeometric function

KW - Mittag-Leffler function

KW - Riemann-Liouville fractional derivative operator

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BT - Extended Hypergeometric Functions and Orthogonal Polynomials

PB - Elsevier

ER -

Some extended-type hypergeometric functions of two and three variables

Abstract

Keywords

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