Some results of extended beta function and hypergeometric functions by using wiman’s function

Shilpi Jain; Rahul Goyal; Praveen Agarwal; Antonella Lupica; Clemente Cesarano

doi:10.3390/math9222944

Some results of extended beta function and hypergeometric functions by using wiman’s function

Shilpi Jain
, Rahul Goyal
, Praveen Agarwal
, Antonella Lupica
, Clemente Cesarano

Nonlinear Dynamic Research Centre (NDRC)

Poornima College of Engineering
International College of Engineering
Harish Chandra Research Institute
International Center for Basic and Applied Sciences
Tuscia University
International Telematic University Uninettuno

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

The main aim of this research paper is to introduce a new extension of the Gauss hypergeometric function and confluent hypergeometric function by using an extended beta function. Some functional relations, summation relations, integral representations, linear transformation formulas, and derivative formulas for these extended functions are derived. We also introduce the logarithmic convexity and some important inequalities for extended beta function.

Original language	English
Article number	2944
Journal	Mathematics
Volume	9
Issue number	22
DOIs	https://doi.org/10.3390/math9222944
State	Published - 1 Nov 2021

Keywords

Classical Euler beta function
Confluent hypergeometric function
Gamma function
Gauss hypergeometric function
Mittag-Leffler function

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10.3390/math9222944

Cite this

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abstract = "The main aim of this research paper is to introduce a new extension of the Gauss hypergeometric function and confluent hypergeometric function by using an extended beta function. Some functional relations, summation relations, integral representations, linear transformation formulas, and derivative formulas for these extended functions are derived. We also introduce the logarithmic convexity and some important inequalities for extended beta function.",

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AU - Lupica, Antonella

AU - Cesarano, Clemente

PY - 2021/11/1

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AB - The main aim of this research paper is to introduce a new extension of the Gauss hypergeometric function and confluent hypergeometric function by using an extended beta function. Some functional relations, summation relations, integral representations, linear transformation formulas, and derivative formulas for these extended functions are derived. We also introduce the logarithmic convexity and some important inequalities for extended beta function.

KW - Classical Euler beta function

KW - Confluent hypergeometric function

KW - Gamma function

KW - Gauss hypergeometric function

KW - Mittag-Leffler function

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DO - 10.3390/math9222944

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Some results of extended beta function and hypergeometric functions by using wiman’s function

Abstract

Keywords

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