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Some new identities for a continued fraction of Ramanujan

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Abstract

We prove some theta-function identities for a continued fraction M(q) of Ramanujan. Then these identities are used to prove modular identities connecting M(q) and \(M(q^n)\) for \(n=\) 2, 3, 5, and 7. We also offer general theorems and reciprocity formula for the explicit evaluation of M(q).

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Authors and Affiliations

  1. Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh, 791112, Arunachal Pradesh, India

    Nipen Saikia

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  1. Nipen Saikia
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Correspondence to Nipen Saikia.

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Saikia, N. Some new identities for a continued fraction of Ramanujan. Ann Univ Ferrara 62, 151–164 (2016). https://doi.org/10.1007/s11565-016-0239-x

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  • DOI: https://doi.org/10.1007/s11565-016-0239-x

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