A study on certain properties of generalized special functions defined by Fox-Wright function

In this study, motivated by the frequent use of Fox-Wright function in the theory of special functions, we first introduced new generalizations of gamma and beta functions with the help of Fox-Wright function. Then by using these functions, we defined generalized Gauss hypergeometric function and ge...

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Bibliographic Details
Published in:Applied mathematics and nonlinear sciences Vol. 5; no. 1; pp. 147 - 162
Main Authors: Ata, Enes, Kıymaz, İ. Onur
Format: Journal Article
Language:English
Published: Beirut Sciendo 01.01.2020
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
Subjects:
33B15
33C015
33C05
Beta function
Confluent hypergeometric function
Fox-Wright function
Gamma function
Gauss hypergeometric function
ISSN:2444-8656, 2444-8656
Online Access:Get full text
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Summary:In this study, motivated by the frequent use of Fox-Wright function in the theory of special functions, we first introduced new generalizations of gamma and beta functions with the help of Fox-Wright function. Then by using these functions, we defined generalized Gauss hypergeometric function and generalized confluent hypergeometric function. For all the generalized functions we have defined, we obtained their integral representations, summation formulas, transformation formulas, derivative formulas and difference formulas. Also, we calculated the Mellin transformations of these functions.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:2444-8656
2444-8656
DOI:10.2478/amns.2020.1.00014