On the reciprocity theorem of Ramanujan and its applications


Abstract


In this paper, we give two new proofs of the reciprocity theorem of Ramanujan found in his lost notebook. We derive the well-known quintuple product identity using the reciprocity theorem. Further we obtain two interesting partition theoretic identities from the reciprocity theorem.

DOI Code: 10.1285/i15900932v38n2p117

Keywords: Basic hypergeometric series; reciprocity theorem; Jacobi's triple product identity; quintuple product identity; partition function

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