Ramanujan's ''lost'' notebook. V: Euler's partition identity
type: Item
instance of: scholarly article
title: Ramanujan's ''lost'' notebook. V: Euler's partition identity
zbMATH Open document ID: 0601.10007
DOI: 10.1016/0001-8708(86)90072-1
published in: Advances in Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Let \(S(m,q)=\prod_{1\leq n\leq m}(1+q^ n)\), and \(T(m,q)=\prod_{1\leq n\leq m}(1-q^{2n-1})^{-1}\). Euler noted that \(S(\infty,q)=T(\infty,q)\). In this note, the author proves two identities from Ramanujan's ''lost'' notebook, expansions of \(\sum_{m\geq 0}(S(\infty,q)-S(m,q))\), and \(\sum_{m\geq 0}(T(\infty,q)-T(m,q))\), and sets them in a more general context.
Mathematics Subject Classification ID: 11P81
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 05A17
zbMATH DE Number: 3968665
zbMATH Keywords: partition identities
author: George E. Andrews
reviewed by: David M. Bressoud
MaRDI profile type: Publication
full work available at URL: 0001-8708(86)90072-1
OpenAlex ID: W1972240934
cites work: On generalizations of Euler's partition theorem
cites work: Two Theorems of Euler and a General Partition Theorem
cites work: On the Geometry of Numbers in Elementary Number Theory
cites work: Ramanujan's ``lost'' notebook. I: Partial Theta-functions
cites work: Q3701427
cites work: Some New Results on Partitions
cites work: Sylvester's partition theorem, and a related result
cites work: On a partition theorem of Sylvester
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description: scientific article; zbMATH DE number 3968665