On Ramanujan’s Incomplete Elliptic Integral Identities

E. N. Bhuvan ()
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E. N. Bhuvan: The National Institute of Engineering, (Autonomous under VTU)

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 4, 1737-1751

Abstract: Abstract In his lost notebook, S. Ramanujan recorded incomplete elliptic integral identities of the first kind. In this paper, we give new proofs to Ramanujan’s incomplete elliptic integrals of the first kind for level 5 using the parameter k(q) = R(q)R2(q2), where R(q) is Rogers-Ramanujan continued fraction. Also, we construct new identities for level 5 similar to ones found in Ramanujan’s work. Further, we prove related identities of level 7, using theta function identities.

Keywords: Incomplete elliptic integrals; modular equations; Dedekind eta-function; theta functions; Rogers-Ramanujan continued fraction; 33E05; 11F11 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0493-6

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