Some Results of Extended Beta Function and Hypergeometric Functions by Using Wiman’s Function

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...

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Autores principales:	Shilpi Jain, Rahul Goyal, Praveen Agarwal, Antonella Lupica, Clemente Cesarano
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	classical Euler beta function gamma function Gauss hypergeometric function confluent hypergeometric function Mittag-Leffler function Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/51a938d109a041be81284fe11c942166
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spelling	oai:doaj.org-article:51a938d109a041be81284fe11c9421662021-11-25T18:17:24ZSome Results of Extended Beta Function and Hypergeometric Functions by Using Wiman’s Function10.3390/math92229442227-7390https://doaj.org/article/51a938d109a041be81284fe11c9421662021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2944https://doaj.org/toc/2227-7390The 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.Shilpi JainRahul GoyalPraveen AgarwalAntonella LupicaClemente CesaranoMDPI AGarticleclassical Euler beta functiongamma functionGauss hypergeometric functionconfluent hypergeometric functionMittag-Leffler functionMathematicsQA1-939ENMathematics, Vol 9, Iss 2944, p 2944 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	classical Euler beta function gamma function Gauss hypergeometric function confluent hypergeometric function Mittag-Leffler function Mathematics QA1-939
spellingShingle	classical Euler beta function gamma function Gauss hypergeometric function confluent hypergeometric function Mittag-Leffler function Mathematics QA1-939 Shilpi Jain Rahul Goyal Praveen Agarwal Antonella Lupica Clemente Cesarano Some Results of Extended Beta Function and Hypergeometric Functions by Using Wiman’s Function
description	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.
format	article
author	Shilpi Jain Rahul Goyal Praveen Agarwal Antonella Lupica Clemente Cesarano
author_facet	Shilpi Jain Rahul Goyal Praveen Agarwal Antonella Lupica Clemente Cesarano
author_sort	Shilpi Jain
title	Some Results of Extended Beta Function and Hypergeometric Functions by Using Wiman’s Function
title_short	Some Results of Extended Beta Function and Hypergeometric Functions by Using Wiman’s Function
title_full	Some Results of Extended Beta Function and Hypergeometric Functions by Using Wiman’s Function
title_fullStr	Some Results of Extended Beta Function and Hypergeometric Functions by Using Wiman’s Function
title_full_unstemmed	Some Results of Extended Beta Function and Hypergeometric Functions by Using Wiman’s Function
title_sort	some results of extended beta function and hypergeometric functions by using wiman’s function
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/51a938d109a041be81284fe11c942166
work_keys_str_mv	AT shilpijain someresultsofextendedbetafunctionandhypergeometricfunctionsbyusingwimansfunction AT rahulgoyal someresultsofextendedbetafunctionandhypergeometricfunctionsbyusingwimansfunction AT praveenagarwal someresultsofextendedbetafunctionandhypergeometricfunctionsbyusingwimansfunction AT antonellalupica someresultsofextendedbetafunctionandhypergeometricfunctionsbyusingwimansfunction AT clementecesarano someresultsofextendedbetafunctionandhypergeometricfunctionsbyusingwimansfunction
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Some Results of Extended Beta Function and Hypergeometric Functions by Using Wiman’s Function

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