Inequalities for Mathieu's series and positive definiteness

DOI10.1007/s10476-011-0403-6zbMath1265.33038OpenAlexW2128818629MaRDI QIDQ452846

Viktor P. Zastavnyi

Publication date: 18 September 2012

Published in: Analysis Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10476-011-0403-6

zbMATH Keywords

inequalitiespositive definite functionscompletely monotonic functionsMathieu's series

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Lamé, Mathieu, and spheroidal wave functions (33E10)

Related Items (2)

Asymptotic expansion for generalized Mathieu series ⋮ Generalized Volterra functions, its integral representations and applications to the Mathieu-type series

Cites Work

• Some inequalities related to an inequality of Mathieu
• On Mathieu's inequality
• Asymptotic expansion and continued fraction for Mathieu's series
• Some new bounds for Mathieu's series
• Das Problem der eingespannten rechteckigen elastischen Platte. I: Die biharmonische Randwertaufgabe für das Rechteck
• Über die Reihe \(\sum_{k=1}^\infty\) \({k\over (k^2+c^2)^2}\)
• Extension of a Function from the Exterior of an Interval to a Positive-Definite Function on the Entire Axis and an Approximation Characteristic of the Class W_M^r,b
• Über eine Abschätzung von Mathieu
• On positive definiteness of some functions
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