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A new proof of Ramanujan’s modular equation relating R(q) with R(q 5)

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Abstract

We give a new proof of Ramanujan’s modular identity relating R(q) with R(q 5), where R(q) is the famous Rogers–Ramanujan continued fraction. Our formulation is stronger than those of preceding authors; in particular, we give for the first time identities for the expressions appearing in the numerator and the denominator of Ramanujan’s identity. A related identity for R(q) that has partition-theoretic connections is also proved.

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  1. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL, 61801, USA

    Chadwick Gugg

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  1. Chadwick Gugg
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Gugg, C. A new proof of Ramanujan’s modular equation relating R(q) with R(q 5). Ramanujan J 20, 163–177 (2009). https://doi.org/10.1007/s11139-009-9180-2

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  • DOI: https://doi.org/10.1007/s11139-009-9180-2

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