{"title":"A remarkable basic hypergeometric identity.","authors":"Christian Krattenthaler, Wadim Zudilin","doi":"10.1007/s11139-024-00994-4","DOIUrl":null,"url":null,"abstract":"<p><p>We give a closed form for <i>quotients</i> of truncated basic hypergeometric series where the base <i>q</i> is evaluated at roots of unity.</p>","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"66 3","pages":"48"},"PeriodicalIF":0.6000,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11785618/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ramanujan Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11139-024-00994-4","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/1/31 0:00:00","PubModel":"Epub","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We give a closed form for quotients of truncated basic hypergeometric series where the base q is evaluated at roots of unity.
期刊介绍：
The Ramanujan Journal publishes original papers of the highest quality in all areas of mathematics influenced by Srinivasa Ramanujan. His remarkable discoveries have made a great impact on several branches of mathematics, revealing deep and fundamental connections.
The following prioritized listing of topics of interest to the journal is not intended to be exclusive but to demonstrate the editorial policy of attracting papers which represent a broad range of interest:
Hyper-geometric and basic hyper-geometric series (q-series) * Partitions, compositions and combinatory analysis * Circle method and asymptotic formulae * Mock theta functions * Elliptic and theta functions * Modular forms and automorphic functions * Special functions and definite integrals * Continued fractions * Diophantine analysis including irrationality and transcendence * Number theory * Fourier analysis with applications to number theory * Connections between Lie algebras and q-series.
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