On the coefficients of asymptotic expansion for the harmonic number by Ramanujan

DOI10.1007/s11139-015-9670-3zbMath1339.41037OpenAlexW2039322052WikidataQ60692025 ScholiaQ60692025MaRDI QIDQ282986

Chao-Ping Chen

Publication date: 13 May 2016

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-015-9670-3

zbMATH Keywords

asymptotic expansionEuler-Mascheroni constantharmonic number

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60)

Related Items

On the Ramanujan harmonic number expansion ⋮ Harmonic number expansions of the Ramanujan type ⋮ Riordan array approach to the coefficients of Ramanujan's harmonic number expansion ⋮ Asymptotic expansions and continued fraction approximations for harmonic numbers ⋮ Ramanujan's formula for the harmonic number ⋮ Optimizing the coefficients of the Ramanujan expansion ⋮ Approximation formulas and inequalities for the Euler-Mascheroni constant ⋮ Ramanujan's harmonic number expansion and two identities for Bernoulli numbers ⋮ Asymptotic series related to Ramanujan's expansion for the harmonic number

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Cites Work

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• 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
• The special functions and their approximations. Vol. I, II
• Stirling expansions into negative powers of a triangular number
• On the harmonic number expansion by Ramanujan
• Asymptotic formulae associated with the Wallis power function and digamma function
• Ramanujan's Harmonic Number Expansion into Negative Powers of a Triangular Number