The Ramanujan Journal

, Volume 38, Issue 1, pp 123–128 | Cite as

Ramanujan’s asymptotic expansion for the harmonic numbers

  • Chao-Ping Chen
  • Jun-Xiang Cheng


In this paper, we provide a recurrence relation for determining the coefficients of Ramanujan’s asymptotic expansion for the \(n\)th harmonic number.


Harmonic numbers Euler–Mascheroni constant Asymptotic expansion 

Mathematics Subject Classification

Primary 41A60 40A25 



The authors thank the referees for their careful reading of the manuscript and insightful comments.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of Mathematics and InformaticsHenan Polytechnic UniversityJiaozuoChina

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