Some extensions of the Fermi-Dirac and Bose-Einstein functions with applications to the family of the zeta and related functions

被引：0
作者：
H. M. Srivastava
M. A. Chaudhry
A. Qadir
A. Tassaddiq
机构：
[1] University of Victoria Victoria,Department of Mathematics
[2] King Fahd University of Petroleum and Minerals,Department of Mathematics and Statistics
[3] National University of Sciences and Technology,Center for Advanced Mathematics and Physics
来源：
Russian Journal of Mathematical Physics | 2011年 / 18卷
关键词：
Mathematical Physic; Zeta Function; Series Representation; Riemann Zeta Function; Extended Function;
D O I：
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学科分类号：
摘要：
The familiar Fermi-Dirac and Bose-Einstein functions are of importance not only for their rôle in quantum statistics, but also for their several interesting mathematical properties in themselves. Here, in our present investigation, we have extended these functions by introducing an extra parameter in a way that gives new insights into these functions and their relationship to the family of zeta functions. These extensions are dual to each other in a sense that is explained in this paper. Some identities are proved here for each of these general functions and their relationship with the general Hurwitz-Lerch zeta function Φ(z, s, a) is exploited to derive some other (presumably new) identities.
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页码：107 / 121
页数：14
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