Degenerate Analogues of Euler Zeta, Digamma, and Polygamma Functions

Degenerate Analogues of Euler Zeta, Digamma, and Polygamma Functions

In recent years, much attention has been paid to the role of degenerate versions of special functions and polynomials in mathematical physics and engineering. In the present paper, we introduce a degenerate Euler zeta function, a degenerate digamma function, and a degenerate polygamma function. We p...

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Main Authors: Fuli He, Ahmed Bakhet, Mohamed Akel, Mohamed Abdalla
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2020/8614841
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spelling doaj-44f7c4ebb37b401fa4c8ef50b0a7d7742020-11-25T02:53:03ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472020-01-01202010.1155/2020/86148418614841Degenerate Analogues of Euler Zeta, Digamma, and Polygamma FunctionsFuli He0Ahmed Bakhet1Mohamed Akel2Mohamed Abdalla3School of Mathematics and Statistics, Central South University, Changsha 410083, ChinaSchool of Mathematics and Statistics, Central South University, Changsha 410083, ChinaDepartment of Mathematics, Faculty of Science, South Valley University, Qena 83523, EgyptDepartment of Mathematics, Faculty of Science, South Valley University, Qena 83523, EgyptIn recent years, much attention has been paid to the role of degenerate versions of special functions and polynomials in mathematical physics and engineering. In the present paper, we introduce a degenerate Euler zeta function, a degenerate digamma function, and a degenerate polygamma function. We present several properties, recurrence relations, infinite series, and integral representations for these functions. Furthermore, we establish identities involving hypergeometric functions in terms of degenerate digamma function.http://dx.doi.org/10.1155/2020/8614841
collection DOAJ
language English
format Article
sources DOAJ
author Fuli He
Ahmed Bakhet
Mohamed Akel
Mohamed Abdalla
spellingShingle Fuli He
Ahmed Bakhet
Mohamed Akel
Mohamed Abdalla
Degenerate Analogues of Euler Zeta, Digamma, and Polygamma Functions
Mathematical Problems in Engineering
author_facet Fuli He
Ahmed Bakhet
Mohamed Akel
Mohamed Abdalla
author_sort Fuli He
title Degenerate Analogues of Euler Zeta, Digamma, and Polygamma Functions
title_short Degenerate Analogues of Euler Zeta, Digamma, and Polygamma Functions
title_full Degenerate Analogues of Euler Zeta, Digamma, and Polygamma Functions
title_fullStr Degenerate Analogues of Euler Zeta, Digamma, and Polygamma Functions
title_full_unstemmed Degenerate Analogues of Euler Zeta, Digamma, and Polygamma Functions
title_sort degenerate analogues of euler zeta, digamma, and polygamma functions
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2020-01-01
description In recent years, much attention has been paid to the role of degenerate versions of special functions and polynomials in mathematical physics and engineering. In the present paper, we introduce a degenerate Euler zeta function, a degenerate digamma function, and a degenerate polygamma function. We present several properties, recurrence relations, infinite series, and integral representations for these functions. Furthermore, we establish identities involving hypergeometric functions in terms of degenerate digamma function.
url http://dx.doi.org/10.1155/2020/8614841
work_keys_str_mv AT fulihe degenerateanaloguesofeulerzetadigammaandpolygammafunctions
AT ahmedbakhet degenerateanaloguesofeulerzetadigammaandpolygammafunctions
AT mohamedakel degenerateanaloguesofeulerzetadigammaandpolygammafunctions
AT mohamedabdalla degenerateanaloguesofeulerzetadigammaandpolygammafunctions
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