New inequalities for some generalized Mathieu type series and the Riemann zeta function

DOI10.7153/jmi-2018-12-13zbMath1391.33007OpenAlexW2791985402MaRDI QIDQ4565877

Khaled Mehrez, Živorad Tomovski, Hari M. Srivastava

Publication date: 13 June 2018

Published in: Journal of Mathematical Inequalities (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.7153/jmi-2018-12-13

zbMATH Keywords

Riemann zeta functioninequalitiesBessel functionTurán-type inequalitiesMathieu seriesgeneralized Mathieu seriesMellin and Laplace integral representations

Mathematics Subject Classification ID

Characteristic functions; other transforms (60E10) Gamma, beta and polygamma functions (33B15) Other functions defined by series and integrals (33E20) Hurwitz and Lerch zeta functions (11M35)

Related Items (9)

Fractional calculus involving \((p, q)\)-Mathieu type series ⋮ Asymptotics of some generalized Mathieu series ⋮ Generalized Volterra functions, its integral representations and applications to the Mathieu-type series ⋮ New integral representations for the Fox-Wright functions and its applications ⋮ Unnamed Item ⋮ Generalization of the quotient mean series ⋮ New properties for several classes of functions related to the Fox-Wright functions ⋮ Monotonicity patterns and functional inequalities for classical and generalized Wright functions ⋮ On a new (p,q)-Mathieu-type power series and its applications

Cites Work

• New upper bounds for Mathieu-type series
• Mathieu series and associated sums involving the zeta functions
• A probabilistic interpretation of complete monotonicity
• On Mathieu's inequality
• Some Mathieu-type series associated with the Fox-Wright function
• Some families of Mathieu \(\mathbf a\)-series and alternating Mathieu \(\mathbf a\)-series
• Das Problem der eingespannten rechteckigen elastischen Platte. I: Die biharmonische Randwertaufgabe für das Rechteck
• 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 families of generalized Mathieu-type power series, associated probability distributions and related inequalities involving complete monotonicity and log-convexity
• On Absolute Convergence of Multiple Fourier Series
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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