Taylor expansions of analytic functions related to \((1+z)^ x-1\)
type: Item
instance of: scholarly article
title: Taylor expansions of analytic functions related to \((1+z)^ x-1\)
zbMATH Open document ID: 0646.30002
DOI: 10.1016/0022-247X(88)90060-1
author: Pavel G. Todorov
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: The author studies the MacLaurin coefficients of functions related to \((1+z)^ x-1\), where \(x\in {\mathbb{C}}\) is arbitrary. He gives recurrence relations and explicit representation formulas, some of which depend on the Stirling numbers \(S(n,k)\) and \(s(n,k)\) of the second and the first kind respectively, which are defined by \[ (k!)^{-1}(e^ z-1)^ k=\sum^{\infty}_{n=k}S(n,k)z^ n/n! \] and \[ (k!)^{-1}(\ell n(1+z))^ k=\sum^{\infty}_{n=k}s(n,k)z^ n/n!. \]
reviewed by: W. Koepf
Mathematics Subject Classification ID: 30B10
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 33E99
zbMATH DE Number: 4053978
zbMATH Keywords: Hermite formula
zbMATH Keywords: Vandermonde convolution
zbMATH Keywords: Lagrange formula
zbMATH Keywords: generating function
zbMATH Keywords: Stirling numbers
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4053978