Asymptotic expansion and continued fraction for Mathieu's series

DOI10.1007/BF01848090zbMath0504.41025OpenAlexW2002995207MaRDI QIDQ1836114

Yanyan Li

Publication date: 1982

Published in: Periodica Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01848090

zbMATH Keywords

two-point continued fraction

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Computation of special functions and constants, construction of tables (65D20) Other special functions (33E99) Convergence and divergence of continued fractions (40A15)

Related Items (11)

On Mathieu's inequality ⋮ Asymptotic expansion for generalized Mathieu series ⋮ Inequalities for Mathieu's series and positive definiteness ⋮ Asymptotics of some generalized Mathieu series ⋮ Some remarks on the Mathieu series ⋮ On Mathieu-type series whose terms contain a generalized hypergeometric function \(_pF_q\) and Meijer's \(G\)-function ⋮ Some new bounds for Mathieu's series ⋮ Integral representations and summations of the modified Struve function ⋮ Some families of Mathieu \(\mathbf a\)-series and alternating Mathieu \(\mathbf a\)-series ⋮ Accurate approximations of the Mathieu series ⋮ Mathieu series and associated sums involving the zeta functions

Cites Work

• Über die Reihe \(\sum_{k=1}^\infty\) \({k\over (k^2+c^2)^2}\)
• Continued Fractions which Correspond to Power Series Expansions at Two Points
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