Several Explicit Evaluations for Ratios of Ramanujan’s Theta Function φ(q)
نویسندگان
چکیده
In this paper we first give alternative proofs of two Ramanujan’s theta function identities. Then we derive several explicit evaluations for ratios of Ramanujan’s theta function φ(q). Mathematics Subject Classification: 11A55, 11F20, 11F27
منابع مشابه
Mock Theta Functions and Quantum Modular Forms
Ramanujan’s last letter to Hardy concerns the asymptotic properties of modular forms and his ‘mock theta functions’. For the mock theta function f (q), Ramanujan claims that as q approaches an even-order 2k root of unity, we have f (q)− (−1)(1− q)(1− q)(1− q) · · · (1− 2q+ 2q − · · ·)= O(1). We prove Ramanujan’s claim as a special case of a more general result. The implied constants in Ramanuja...
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