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arXiv · 2506.01181

Ninth degree analogue of Ramanujan's septic theta function identity

Sun Kim·Örs Rebák
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Abstract

On page 206 in his lost notebook, Ramanujan recorded a seventh degree identity for his theta function $\varphi(q)$. We give an analogous ninth degree identity. We also provide an application of an entry from his second notebook on a cubic equation and an interpretation with theta functions for some of his trigonometric identities. Lastly, we calculate five examples for $\varphi(e^{-\pi\sqrt{n}})$.

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Sun Kim, Örs Rebák. 2025-06-01. Ninth degree analogue of Ramanujan's septic theta function identity. https://arxiv.org/abs/2506.01181

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