Expanding the function \(\ln(1 + \operatorname{e}^x)\) into power series in terms of the Dirichlet eta function and the Stirling numbers of the second kind
type: Item
instance of: scholarly article
title: Expanding the function \(\ln(1 + \operatorname{e}^x)\) into power series in terms of the Dirichlet eta function and the Stirling numbers of the second kind
zbMATH Open document ID: 1548.4103
author: Wenhui Li
author: Dongkyu Lim
author: Feng Qi
published in: Carpathian Mathematical Publications
publication date: 2024-08-19T00:00:00Z
review text: The authors provide several simple and alternative proofs of the conjecture proposed by G. Helms in the year 2013. They expand the composite function into power series whose coefficients are expressed in terms of the Dirichlet eta function and the Stirling numbers of the second kind.
reviewed by: Neha Malik
Mathematics Subject Classification ID: 41A58
Mathematics Subject Classification ID: 11B73
Mathematics Subject Classification ID: 11M06
Mathematics Subject Classification ID: 11M41
zbMATH DE Number: 7898637
zbMATH Keywords: Dirichlet eta function
zbMATH Keywords: composite function
zbMATH Keywords: power series expansion
zbMATH Keywords: Stirling number of second kind
zbMATH Keywords: Riemann zeta function
zbMATH Keywords: partial Bell polynomial
MaRDI profile type: Publication
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DOI: 10.15330/CMP.16.1.320-327
description: scientific article; zbMATH DE number 7898637