Two complementary relations for the Rogers-Ramanujan continued fraction

preprint2021arXivOpen access

Let $R(q)$ be the Rogers-Ramanujan continued fraction. We give different proofs of two complementary relations for $R(q)$ given by Ramanujan and proved by Watson and Ramanathan. Our proofs only use product expansions for classical Jacobi theta functions.

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Two complementary relations for the Rogers-Ramanujan continued fraction

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