On the Ramanujan harmonic number expansion

DOI10.1007/s00025-018-0925-3zbMath1440.11025OpenAlexW2901382815MaRDI QIDQ1633389

Chao-Ping Chen

Publication date: 19 December 2018

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-018-0925-3

zbMATH Keywords

asymptotic expansionEuler-Mascheroni constantharmonic number

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Convergence and divergence of series and sequences (40A05) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60)

Related Items (4)

The Schwarzian derivative on Finsler manifolds of constant curvature ⋮ Asymptotic expansions and continued fraction approximations for harmonic numbers ⋮ Optimizing the coefficients of the Ramanujan expansion ⋮ Some Bohr-type inequalities with one parameter for bounded analytic functions

Cites Work

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• On the coefficients of asymptotic expansion for the harmonic number by Ramanujan
• Ramanujan's enigmatic formula for the harmonic series
• Asymptotic expansion for \(\log n!\) in terms of the reciprocal of a triangular number
• Ramanujan's asymptotic expansion for the harmonic numbers
• On the Ramanujan-Lodge harmonic number expansion
• Riordan array approach to the coefficients of Ramanujan's harmonic number expansion
• Ramanujan's formula for the harmonic number
• Stirling expansions into negative powers of a triangular number
• On the harmonic number expansion by Ramanujan
• Ramanujan's Harmonic Number Expansion into Negative Powers of a Triangular Number
• An asymptotic series related to Ramanujan's expansion for the \(n\)th harmonic number

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