Expanding the function ln⁡(1+ex) into power series in terms of the Dirichlet eta function and the Stirling numbers of the second kind

Authors

  • Wen-Hui Li Henan Kaifeng College of Science Technology and Communication, Kaifeng 475001, Henan, China
  • Dongkyu Lim Andong National University, Andong 36729, Republic of Korea
  • Feng Qi Hulunbuir University, Inner Mongolia, China; Henan Polytechnic University, Jiaozuo 454010, Henan, China https://orcid.org/0000-0001-6239-2968
https://doi.org/10.15330/cmp.16.1.320-327

Keywords:

Dirichlet eta function, composite function, power series expansion, Stirling number of the second kind, Riemann zeta function, partial Bell polynomial
Published online: 2024-06-30

Abstract

In the paper, using several approaches, the authors expand the composite function ln⁡(1+ex) into power series around x=0, whose coefficients are expressed in terms of the Dirichlet eta function η(1−n) and the Stirling numbers of the second kind S(n,k).

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How to Cite
(1)
Li, W.-H.; Lim, D.; Qi, F. Expanding the Function ln⁡(1+ex) into Power Series in Terms of the Dirichlet Eta Function and the Stirling Numbers of the Second Kind. Carpathian Math. Publ. 2024, 16, 320-327.