Two-sided inequalities for the extended Hurwitz–Lerch Zeta function

Recently, Srivastava et al. (2011)  [2] unified and extended several interesting generalizations of the familiar Hurwitz–Lerch Zeta function Φ ( z , s , a ) by introducing a Fox–Wright type generalized hypergeometric function in the kernel. For this newly introduced special function, two integral re...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2011-07, Vol.62 (1), p.516-522
Main Authors: Srivastava, H.M., Jankov, Dragana, Pogány, Tibor K., Saxena, R.K.
Format: Article
Language:English
Subjects:
Extended Hurwitz–Lerch Zeta function
Fox–Wright [formula omitted] function
Hypergeometric [formula omitted] function
Inequalities
Integrals
Kernels
Mathematical analysis
Mathematical models
Mathieu [formula omitted]-series techniques
Psi (or Digamma) function
Representations
Two-sided bounding inequalities
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Summary:Recently, Srivastava et al. (2011)  [2] unified and extended several interesting generalizations of the familiar Hurwitz–Lerch Zeta function Φ ( z , s , a ) by introducing a Fox–Wright type generalized hypergeometric function in the kernel. For this newly introduced special function, two integral representations of different kinds are investigated here by means of a known result involving a Fox–Wright generalized hypergeometric function kernel, which was given earlier by Srivastava et al. (2011)  [2], and by applying some Mathieu ( a , λ ) -series techniques. Finally, by appealing to each of these two integral representations, two sets of two-sided bounding inequalities are proved, thereby extending and generalizing the recent work by Jankov et al. (2011)  [15].
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2011.05.035