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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Vydáno v:Applied mathematics and nonlinear sciences Ročník 5; číslo 1; s. 147 - 162
Hlavní autoři: Ata, Enes, Kıymaz, İ. Onur
Médium: Journal Article
Jazyk:angličtina
Vydáno: Beirut Sciendo 01.01.2020
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
Témata:
33B15
33C015
33C05
Beta function
Confluent hypergeometric function
Fox-Wright function
Gamma function
Gauss hypergeometric function
ISSN:2444-8656, 2444-8656
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:2444-8656
2444-8656
DOI:10.2478/amns.2020.1.00014