A proof of Pollaczek-Spitzer identity
type: Item
instance of: scholarly article
title: A proof of Pollaczek-Spitzer identity
zbMATH Open document ID: 0731.60064
DOI: 10.1155/S0161171290001004
author: S. Paramasamy
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46609
review text: First, the author proves the following generalization of Takacs' ballot theorem. If \(r_ 1,r_ 2,...,r_ n\) are integers with sum \(s\geq 1\) and \(n_ r\) denotes the number of cyclic permutations in which all the partial sums are greater or equal to r with at least one sum equal to r, then \(\sum^{s}_{r=1}rn_ r=s\). Then this result is used to give a short (seemingly new) proof of the well-known Pollaczek-Spitzer identity.
reviewed by: S.Grigorescu
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 4209243
zbMATH Keywords: ballot theorem
zbMATH Keywords: Pollaczek-Spitzer identity
MaRDI profile type: Publication
OpenAlex ID: W2084647068
description: scientific article; zbMATH DE number 4209243