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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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 |
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1715360651623268352 |