Properties and applications of the reciprocal logarithm numbers
type: Item
instance of: scholarly article
title: Properties and applications of the reciprocal logarithm numbers
zbMATH Open document ID: 1208.11032
author: Victor Kowalenko
published in: Acta Applicandae Mathematicae
publication date: 2010-04-23T00:00:00Z
review text: The author investigates the sequence of rational numbers \((A_k)_{k\geq 0}\), which he calls the ``reciprocal logarithm numbers'' defined by the series expansion \(1/\ln(1+z) = \sum_{k=0}^\infty A_k z^{k-1}\). He derives several properties of these numbers such as recursions, integral representations and identities. More specifically, he points out the relationship of the \(A_k\)'s to Stirling numbers of the first kind and to Euler's constant. A similar approach is then presented for the series expansion of \(1/\arctan x\).
reviewed by: Thomas Stoll
Mathematics Subject Classification ID: 11B73
Mathematics Subject Classification ID: 41A58
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 05C90
zbMATH DE Number: 5700597
zbMATH Keywords: Euler's constant
zbMATH Keywords: harmonic numbers
zbMATH Keywords: power series expansions
zbMATH Keywords: reciprocal logarithm numbers
zbMATH Keywords: recursion relation
describes a project that uses: Mathematica
describes a project that uses: OEIS
MaRDI profile type: Publication
full work available at URL: s10440-008-9325-0
OpenAlex ID: W2037419927
Wikidata QID: Q60691962
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DOI: 10.1007/S10440-008-9325-0
description: scientific article; zbMATH DE number 5700597