On incomplete elliptic integrals related to Ramanujan's theta functions
type: Item
instance of: scholarly article
title: On incomplete elliptic integrals related to Ramanujan's theta functions
author: K. R. Vasuki
author: Guillaume Vinay
published in: The Journal of Analysis
publication date: 2022-10-27T00:00:00Z
review text: In his lost notebook Ramanujan mentioned on pages 51-53 certain incomplete elliptic integral identities of first kind. By using theory of modular forms, \textit{S. Raghavan} and \textit{S. S. Rangachari} [in: Number theory and related topics. Papers presented at the Ramanujan birth centenary international colloquium, Bombay, India, 4-11 January, 1988. Oxford: Oxford University Press, published for the Tata Institute of Fundamental Research. 119--149 (1989; Zbl 0748.33013)] had proved Ramanujan's elliptic integral identities. These identities were also proved by \textit{B. C. Berndt} et al. [Contemp. Math. 254, 79--126 (2000; Zbl 0971.33012)] by using another methods. It has been observed a common fact in both proofs that it is setting up some differential equations satisfied by the theta function in consideration. Using this, the authors establish and prove three new incomplete elliptic integrals of first kind.
Mathematics Subject Classification ID: 11F20
Mathematics Subject Classification ID: 33C75
Mathematics Subject Classification ID: 33E05
Mathematics Subject Classification ID: 33C05
zbMATH DE Number: 7608550
zbMATH Keywords: modular equations
zbMATH Keywords: theta functions
zbMATH Keywords: incomplete elliptic integrals
zbMATH Keywords: Eisenstein series
reviewed by: C. L. Parihar
MaRDI profile type: Publication
full work available at URL: s41478-022-00414-0
OpenAlex ID: W4220952631
Wikidata QID: Q114217538
cites work: Q4000402
cites work: Q4502700
cites work: Ramanujan's Theta Functions
cites work: Q4012862
cites work: Q5513003
cites work: Q4040264
cites work: “cases? for φ also” a question raised by Ramanujan
cites work: On certain new differential equations for ratio of theta functions
DOI: 10.1007/S41478-022-00414-0
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description: scientific article; zbMATH DE number 7608550