In his Lost Notebook, Ramanujan claimed that the "circular" summation of the n-th powers of the symmetric theta function f(a, b) satisfies a factorization of the form f(a, b)F n(ab). Moreover, Ramanujan recorded identities expressing F 2(q), F 3(q), F 4(q), F 5(q), and F 7(q) in terms of his theta functions φ(q), ψ(q), and f(-q). Ramanujan's claims were proved by Rangachari, and later (via elementary methods) by Son. In this paper we obtain similar identities for F 6(q), F 8(q), F 9(q), and F 10(q).
|Original language||English (US)|
|Number of pages||6|
|Journal||Proceedings of the American Mathematical Society|
|State||Published - 2000|
- Theta functions
ASJC Scopus subject areas
- Applied Mathematics