Integral expressions for Mathieu-type power series and for the Butzer-Flocke-Hauss Ω-function

DOI10.2478/s13540-011-0036-2zbMath1273.33016OpenAlexW2095327044MaRDI QIDQ2853368

Živorad Tomovski, Tibor K. Pogáni

Publication date: 21 October 2013

Published in: Fractional Calculus and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s13540-011-0036-2

zbMATH Keywords

Fourier sine transformBessel function of the first kindconfluent hypergeometric functiongeneralized Mathieu seriesalternating generalized Mathieu series

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Integral transforms of special functions (44A20) Other functions defined by series and integrals (33E20) Generalized hypergeometric series, ({}_pF_q) (33C20) Convergence and divergence of integrals (40A10)

Related Items (12)

Alternating Mathieu Series, Hilbert–Eisenstein Series and Their Generalized Omega Functions ⋮ Certain generalized fractional calculus formulas and integral transforms involving \((p, q)\)-Mathieu-type series ⋮ Computable solution of fractional kinetic equations using Mathieu-type 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 \(Y_{\nu}\) ⋮ Certain fractional calculus formulas involving extended generalized Mathieu series ⋮ Asymptotics of some generalized Mathieu series ⋮ Multi-parameter Mathieu, and alternating Mathieu series ⋮ Solution of fractional kinetic equations associated with the \((p, q)\)-Mathieu-type series ⋮ Fractional integration and differentiation of the generalized Mathieu series ⋮ Asymptotic expansion of Mathieu power series and trigonometric Mathieu series ⋮ A note on fractional Bessel equation and its asymptotics

Cites Work

• Mathieu series and associated sums involving the zeta functions
• Some inequalities related to an inequality of Mathieu
• A linear ODE for the Omega function associated with the Euler function \(E_{\alpha}(z)\) and the Bernoulli function \(B_{\alpha }(z)\)
• 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 representations and integral transforms of some families of Mathieu type series
• Some two-sided bounding inequalities for the Butzer-Flocke-Hauss omega function
• New integral and series representations of the generalized Mathieu series
• All the special functions are fractional differintegrals of elementary functions
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