Polylogarithms in the theory of univalent functions
type: Item
instance of: scholarly article
title: Polylogarithms in the theory of univalent functions
zbMATH Open document ID: 0863.30016
DOI: 10.1007/BF03322186
author: Saminathan Ponnusamy
author: S. Sabapathy
published in: Results in Mathematics
publication date: 1997-05-27T00:00:00Z
review text: Let \(a,b> -1,p\) and \(q\) nonzero real numbers such that \(p+q \geq 1\). In this paper, the authors study geometric mapping properties of the (normalized) generalized polylogarithm defined in the unit disk \(\Delta = \{z\in\mathbb{C}: |z |< 1\}\) by \[ \Phi_{p,q} (a,b; z) = \sum^\infty_{n=1} {(1+ a)^p(1+ b)^q \over (n+ a)^p(n+ b)^q} z^n = z + \dots. \] Under various parameter restrictions the authors prove several results concerning the membership of the function \(\Phi_{p,q} (a,b;z)\) in the well-known subclasses of univalent functions such as the class \(K_1 \cap S^*\).
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 33C20
zbMATH DE Number: 933262
zbMATH Keywords: generalized polylogarithm
reviewed by: M. Vuorinen
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 933262