### Abstract

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) |
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Pages (from-to) | 1333-1338 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 128 |

Issue number | 5 |

State | Published - 2000 |

Externally published | Yes |

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### Keywords

- Ramanujan
- Theta functions

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics