<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

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

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

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...

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

Publié en ligne: 31 mars 2020

Pages: 147 - 162

Reçu: 26 mars 2019

Accepté: 08 avr. 2019

DOI: https://doi.org/10.2478/amns.2020.1.00014

Mots clés
Gamma function, Beta function, Fox-Wright function, Gauss hypergeometric function, Confluent hypergeometric function

© 2019 Enes Ata et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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

Publié en ligne: 31 mars 2020

Pages: 147 - 162

Reçu: 26 mars 2019

Accepté: 08 avr. 2019

DOI: https://doi.org/10.2478/amns.2020.1.00014

Mots clésGamma function, Beta function, Fox-Wright function, Gauss hypergeometric function, Confluent hypergeometric function

© 2019 Enes Ata et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Mots clés
Gamma function, Beta function, Fox-Wright function, Gauss hypergeometric function, Confluent hypergeometric function