Ramanujan's asymptotic expansion for the harmonic numbers

DOI10.1007/s11139-014-9575-6zbMath1381.11116OpenAlexW2068530451MaRDI QIDQ746391

Chao-Ping Chen, Jun-Xiang Cheng

Publication date: 16 October 2015

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

Full work available at URL: https://doi.org/10.1007/s11139-014-9575-6

zbMATH Keywords

asymptotic expansionharmonic numbersEuler-Mascheroni constant

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Approximation to limiting values (summation of series, etc.) (40A25) Evaluation of number-theoretic constants (11Y60)

Related Items (11)

On the coefficients of asymptotic expansion for the harmonic number by Ramanujan ⋮ On the Ramanujan harmonic number expansion ⋮ Harmonic number expansions of the Ramanujan type ⋮ Stirling expansions into negative powers of a triangular number ⋮ 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 ⋮ Ramanujan's harmonic number expansion and two identities for Bernoulli numbers ⋮ Structural properties of Dirichlet series with harmonic coefficients ⋮ Asymptotic series related to Ramanujan's expansion for the harmonic number

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Ramanujan's enigmatic formula for the harmonic series
• Asymptotic expansion for \(\log n!\) in terms of the reciprocal of a triangular number
• Asymptotic formulae associated with the Wallis power function and digamma function
• Ramanujan's Harmonic Number Expansion into Negative Powers of a Triangular Number
• Coefficient Identities for Powers of Taylor and Dirichlet Series

This page was built for publication: Ramanujan's asymptotic expansion for the harmonic numbers