Generalization of the Quotient Mean Series
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DOI: 10.1007/s00025-019-1008-9
Abstract: In this paper a new family of generalized Mathieu series, called Quotient mean Matheu series is introduced. Namely, some generalized Mathieu series, like Mathieu $$(a,\lambda )$$(a,λ)-series, Mathieu a-series and their alternating variants are represented in… read more here.
Keywords: quotient mean; generalization quotient; mean series; mathieu series ... See more keywords
Asymptotic expansion of Mathieu power series and trigonometric Mathieu series
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DOI: 10.1016/j.jmaa.2019.07.029
Abstract: We consider a generalized Mathieu series where the summands of the classical Mathieu series are multiplied by powers of a complex number. The Mellin transform of this series can be expressed by the polylogarithm or… read more here.
Keywords: asymptotic expansion; trigonometric mathieu; mathieu; mathieu series ... See more keywords
On generalized Mathieu series and its companions
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DOI: 10.15672/hjms.2018.579
Abstract: Integral representations for a generalized Mathieu series and its companions are used to obtain bounds for their corresponding series. The bounds are procured mainly using results pertaining to the Cebysev functional. The relationship to Zeta… read more here.
Keywords: series companions; mathieu series; series; generalized mathieu ... See more keywords
Hilbert's Double Series Theorem's Extensions via the Mathieu Series Approach
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DOI: 10.3390/axioms11110643
Abstract: The author’s research devoted to the Hilbert’s double series theorem and its various further extensions are the focus of a recent survey article. The sharp version of double series inequality result is extended in the… read more here.
Keywords: series theorem; double series; series; mathieu series ... See more keywords
Generalized Fractional Integral Operators Pertaining to the Product of Srivastava’s Polynomials and Generalized Mathieu Series
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DOI: 10.3390/math7020206
Abstract: Fractional calculus image formulas involving various special functions are important for evaluation of generalized integrals and to obtain the solution of differential and integral equations. In this paper, the Saigo’s fractional integral operators involving hypergeometric… read more here.
Keywords: fractional integral; generalized mathieu; integral operators; product ... See more keywords