On the 2- and 4-dissections of Ramanujan's continued fraction and its reciprocal

Author: Hirschhorn Michael  

Publisher: Springer Publishing Company

ISSN: 1382-4090

Source: The Ramanujan Journal, Vol.24, Iss.1, 2011-01, pp. : 85-92

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Abstract

We present elementary proofs, using only Jacobi's triple product identity, of four identities of Ramanujan and eight identities of Hirschhorn relating to the 2-dissection and the 4-dissection of Ramanujan's continued fraction and its reciprocal, and of two identities from Ramanujan's famous list of forty.