Analysis of a generalized Lebesgue identity in Ramanujan’s Lost Notebook

We analyze a two-parameter q -series identity in Ramanujan’s Lost Notebook that generalizes the product part of the fundamental one-parameter Lebesgue identity. From reformulations of this two-parameter identity, we deduce new partition theorems including variants of the Gauss triangular number iden...

Full description

Saved in:
Bibliographic Details
Published in:The Ramanujan journal 2012-12, Vol.29 (1-3), p.339-358
Main Author: Alladi, Krishnaswami
Format: Article
Language:English
Subjects:
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c321t-3f1bb59732986041a0de2853236e07ea0a1d9408606d5d7fdc7f51fe055d9e163
cites cdi_FETCH-LOGICAL-c321t-3f1bb59732986041a0de2853236e07ea0a1d9408606d5d7fdc7f51fe055d9e163
container_end_page 358
container_issue 1-3
container_start_page 339
container_title The Ramanujan journal
container_volume 29
creator Alladi, Krishnaswami
description We analyze a two-parameter q -series identity in Ramanujan’s Lost Notebook that generalizes the product part of the fundamental one-parameter Lebesgue identity. From reformulations of this two-parameter identity, we deduce new partition theorems including variants of the Gauss triangular number identity and Euler’s pentagonal number theorem. We discuss connections with a partial theta identity of Ramanujan and with several classical results such as those of Sylvester and Göllnitz–Gordon.
doi_str_mv 10.1007/s11139-012-9380-z
format article
fullrecord <record><control><sourceid>crossref_sprin</sourceid><recordid>TN_cdi_crossref_primary_10_1007_s11139_012_9380_z</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1007_s11139_012_9380_z</sourcerecordid><originalsourceid>FETCH-LOGICAL-c321t-3f1bb59732986041a0de2853236e07ea0a1d9408606d5d7fdc7f51fe055d9e163</originalsourceid><addsrcrecordid>eNp9kE1OwzAQRi0EElA4ADtfIDBjx3G8rCp-FYGEYG059aRKaW1kp4t2xTW4HichVVmzmhl980aax9gVwjUC6JuMiNIUgKIwsoZid8TOUOn9BPJ47GUtihIMnLLznJcAUILUZ-xpGtxqm_vMY8cdX1Cg5Fb9jjxvqKW82BDvPYWhH7a8D_zVrV3YLF34-frOvIl54M9xoDbGjwt20rlVpsu_OmHvd7dvs4eiebl_nE2bYi4FDoXssG2V0VKYuoISHXgStZJCVgSaHDj0poQxq7zyuvNz3SnsCJTyhrCSE4aHu_MUc07U2c_Ur13aWgS7l2EPMuwow-5l2N3IiAOTx92woGSXcZPG1_M_0C-jk2NM</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Analysis of a generalized Lebesgue identity in Ramanujan’s Lost Notebook</title><source>Springer Link</source><creator>Alladi, Krishnaswami</creator><creatorcontrib>Alladi, Krishnaswami</creatorcontrib><description>We analyze a two-parameter q -series identity in Ramanujan’s Lost Notebook that generalizes the product part of the fundamental one-parameter Lebesgue identity. From reformulations of this two-parameter identity, we deduce new partition theorems including variants of the Gauss triangular number identity and Euler’s pentagonal number theorem. We discuss connections with a partial theta identity of Ramanujan and with several classical results such as those of Sylvester and Göllnitz–Gordon.</description><identifier>ISSN: 1382-4090</identifier><identifier>EISSN: 1572-9303</identifier><identifier>DOI: 10.1007/s11139-012-9380-z</identifier><language>eng</language><publisher>Boston: Springer US</publisher><subject>Combinatorics ; Field Theory and Polynomials ; Fourier Analysis ; Functions of a Complex Variable ; Mathematics ; Mathematics and Statistics ; Number Theory</subject><ispartof>The Ramanujan journal, 2012-12, Vol.29 (1-3), p.339-358</ispartof><rights>Springer Science+Business Media, LLC 2012</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c321t-3f1bb59732986041a0de2853236e07ea0a1d9408606d5d7fdc7f51fe055d9e163</citedby><cites>FETCH-LOGICAL-c321t-3f1bb59732986041a0de2853236e07ea0a1d9408606d5d7fdc7f51fe055d9e163</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Alladi, Krishnaswami</creatorcontrib><title>Analysis of a generalized Lebesgue identity in Ramanujan’s Lost Notebook</title><title>The Ramanujan journal</title><addtitle>Ramanujan J</addtitle><description>We analyze a two-parameter q -series identity in Ramanujan’s Lost Notebook that generalizes the product part of the fundamental one-parameter Lebesgue identity. From reformulations of this two-parameter identity, we deduce new partition theorems including variants of the Gauss triangular number identity and Euler’s pentagonal number theorem. We discuss connections with a partial theta identity of Ramanujan and with several classical results such as those of Sylvester and Göllnitz–Gordon.</description><subject>Combinatorics</subject><subject>Field Theory and Polynomials</subject><subject>Fourier Analysis</subject><subject>Functions of a Complex Variable</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Number Theory</subject><issn>1382-4090</issn><issn>1572-9303</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><recordid>eNp9kE1OwzAQRi0EElA4ADtfIDBjx3G8rCp-FYGEYG059aRKaW1kp4t2xTW4HichVVmzmhl980aax9gVwjUC6JuMiNIUgKIwsoZid8TOUOn9BPJ47GUtihIMnLLznJcAUILUZ-xpGtxqm_vMY8cdX1Cg5Fb9jjxvqKW82BDvPYWhH7a8D_zVrV3YLF34-frOvIl54M9xoDbGjwt20rlVpsu_OmHvd7dvs4eiebl_nE2bYi4FDoXssG2V0VKYuoISHXgStZJCVgSaHDj0poQxq7zyuvNz3SnsCJTyhrCSE4aHu_MUc07U2c_Ur13aWgS7l2EPMuwow-5l2N3IiAOTx92woGSXcZPG1_M_0C-jk2NM</recordid><startdate>20121201</startdate><enddate>20121201</enddate><creator>Alladi, Krishnaswami</creator><general>Springer US</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20121201</creationdate><title>Analysis of a generalized Lebesgue identity in Ramanujan’s Lost Notebook</title><author>Alladi, Krishnaswami</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c321t-3f1bb59732986041a0de2853236e07ea0a1d9408606d5d7fdc7f51fe055d9e163</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Combinatorics</topic><topic>Field Theory and Polynomials</topic><topic>Fourier Analysis</topic><topic>Functions of a Complex Variable</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Number Theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Alladi, Krishnaswami</creatorcontrib><collection>CrossRef</collection><jtitle>The Ramanujan journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Alladi, Krishnaswami</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Analysis of a generalized Lebesgue identity in Ramanujan’s Lost Notebook</atitle><jtitle>The Ramanujan journal</jtitle><stitle>Ramanujan J</stitle><date>2012-12-01</date><risdate>2012</risdate><volume>29</volume><issue>1-3</issue><spage>339</spage><epage>358</epage><pages>339-358</pages><issn>1382-4090</issn><eissn>1572-9303</eissn><abstract>We analyze a two-parameter q -series identity in Ramanujan’s Lost Notebook that generalizes the product part of the fundamental one-parameter Lebesgue identity. From reformulations of this two-parameter identity, we deduce new partition theorems including variants of the Gauss triangular number identity and Euler’s pentagonal number theorem. We discuss connections with a partial theta identity of Ramanujan and with several classical results such as those of Sylvester and Göllnitz–Gordon.</abstract><cop>Boston</cop><pub>Springer US</pub><doi>10.1007/s11139-012-9380-z</doi><tpages>20</tpages></addata></record>
fulltext fulltext
identifier ISSN: 1382-4090
ispartof The Ramanujan journal, 2012-12, Vol.29 (1-3), p.339-358
issn 1382-4090
1572-9303
language eng
recordid cdi_crossref_primary_10_1007_s11139_012_9380_z
source Springer Link
subjects Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
title Analysis of a generalized Lebesgue identity in Ramanujan’s Lost Notebook
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-01T03%3A58%3A54IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-crossref_sprin&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Analysis%20of%20a%20generalized%20Lebesgue%20identity%20in%20Ramanujan%E2%80%99s%20Lost%20Notebook&rft.jtitle=The%20Ramanujan%20journal&rft.au=Alladi,%20Krishnaswami&rft.date=2012-12-01&rft.volume=29&rft.issue=1-3&rft.spage=339&rft.epage=358&rft.pages=339-358&rft.issn=1382-4090&rft.eissn=1572-9303&rft_id=info:doi/10.1007/s11139-012-9380-z&rft_dat=%3Ccrossref_sprin%3E10_1007_s11139_012_9380_z%3C/crossref_sprin%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c321t-3f1bb59732986041a0de2853236e07ea0a1d9408606d5d7fdc7f51fe055d9e163%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true