Partial reciprocal sums of the Mathieu series

DOI10.1186/S13660-017-1327-XzbMath1372.40002OpenAlexW2593942923WikidataQ42317041 ScholiaQ42317041MaRDI QIDQ517773

Xin Lin

Publication date: 27 March 2017

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-017-1327-x

zbMATH Keywords

elementary methodMathieu seriesreciprocal sums

Mathematics Subject Classification ID

Approximation to limiting values (summation of series, etc.) (40A25)

Related Items (2)

Asymptotic expansion for generalized Mathieu series ⋮ Asymptotic behavior of reciprocal sum of two products of Fibonacci numbers

Cites Work

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• On the reciprocal sums of the generalized Fibonacci sequences
• The sums of the reciprocals of Fibonacci polynomials and Lucas polynomials
• Several identities involving the Fibonacci polynomials and Lucas polynomials
• The infinite sum of reciprocal Pell numbers
• Accurate approximations of the Mathieu series
• Mathieu series and associated sums involving the zeta functions
• On the reciprocal sums of higher-order sequences
• The infinite sum of the cubes of reciprocal pell numbers
• More on the infinite sum of reciprocal Fibonacci, Pell and higher order recurrences
• Das Problem der eingespannten rechteckigen elastischen Platte. I: Die biharmonische Randwertaufgabe für das Rechteck
• Über die Reihe \(\sum_{k=1}^\infty\) \({k\over (k^2+c^2)^2}\)
• Über eine Abschätzung von Mathieu
• Some identities related to Riemann zeta-function

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