Mathieu series and associated sums involving the zeta functions

DOI10.1016/j.camwa.2009.10.008zbMath1189.33036OpenAlexW2085875768MaRDI QIDQ980281

Junesang Choi, Hari M. Srivastava

Publication date: 28 June 2010

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2009.10.008

zbMATH Keywords

Fourier sine transformgamma functionpsi (or digamma) functionHurwitz zeta functionRiemann zeta functionBernoulli numbersEuler-Mascheroni constantMathieu seriesalternating Mathieu seriesDirichlet eta functiontrigamma and polygamma functions

Mathematics Subject Classification ID

Other functions defined by series and integrals (33E20)

Related Items (15)

Multiple Gamma Functions and Their Applications ⋮ Alternating Mathieu Series, Hilbert–Eisenstein Series and Their Generalized Omega Functions ⋮ New inequalities for some generalized Mathieu type series and the Riemann zeta function ⋮ Asymptotic expansion for generalized Mathieu series ⋮ Some families of the general Mathieu‐type series with associated properties and functional inequalities ⋮ Extension of Mathieu series and alternating Mathieu series involving the Neumann function \(Y_{\nu}\) ⋮ A fresh approach to classical Eisenstein series and the newer Hilbert–Eisenstein series ⋮ Multi-parameter Mathieu, and alternating Mathieu series ⋮ Fractional operators associated with the \(\underline{p}\)-extended Mathieu series by using Laplace transform ⋮ Partial reciprocal sums of the Mathieu series ⋮ Accurate approximations of the Mathieu series ⋮ Fractional integration and differentiation of the generalized Mathieu series ⋮ Some two-sided inequalities for multiple Gamma functions and related results ⋮ Geometric properties of Mathieu-type power series inside unit disk ⋮ Integral expressions for Mathieu-type power series and for the Butzer-Flocke-Hauss Ω-function

Cites Work

• On Mathieu-type series whose terms contain a generalized hypergeometric function \(_pF_q\) and Meijer's \(G\)-function
• New upper bounds for Mathieu-type series
• Sums of certain series of the Riemann zeta function
• Some inequalities related to an inequality of Mathieu
• Certain classes of series involving the zeta function
• On Mathieu's inequality
• Certain classes of series associated with the zeta function and multiple gamma functions
• Asymptotic expansion and continued fraction for Mathieu's series
• Integral representation of a series which includes the Mathieu \(\mathbf a\)-series
• Some Mathieu-type series associated with the Fox-Wright function
• Integral expressions for Mathieu-type series whose terms contain Fox's \(H\)-function
• Some families of Mathieu \(\mathbf a\)-series and alternating Mathieu \(\mathbf a\)-series
• Über die Reihe \(\sum_{k=1}^\infty\) \({k\over (k^2+c^2)^2}\)
• Integral representation of Mathieu (a, λ)-series
• Integral representations and integral transforms of some families of Mathieu type series
• Some bounds for alternating Mathieu type series
• New integral and series representations of the generalized Mathieu series
• On multiple generalized Mathieu series
• Some Series Involving the Riemann Zeta Function
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