Abstract
Let f(a, b) denote Ramanujan's symmetric theta function. In his Lost Notebook, Ramanujan claimed that the “circular” summation of n-th powers of f satisfies a factorization of the form f(a, b)F(ab). He listed elegant identities for n = 2, 3, 4, 5 and 7. We present alternative proofs of his claims.
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Son, S.H. Circular Summations of Theta Functions in Ramanujan's Lost Notebook. The Ramanujan Journal 8, 235–272 (2004). https://doi.org/10.1023/B:RAMA.0000040483.55191.d1
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DOI: https://doi.org/10.1023/B:RAMA.0000040483.55191.d1