Some Identities of Ramanujan's q-Continued Fractions of Order Fourteen and Twenty-Eight, and Vanishing Coefficients

Shraddha Rajkhowa; Nipen Saikia

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arXiv · 2305.14988

Some Identities of Ramanujan's q-Continued Fractions of Order Fourteen and Twenty-Eight, and Vanishing Coefficients

Shraddha Rajkhowa·Nipen Saikia

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Abstract

We deduce $q$-continued fractions $S_{1}(q)$, $S_{2}(q)$ and $S_{3}(q)$ of order fourteen, and continued fractions $V_{1}(q)$, $V_{2}(q)$ and $V_{3}(q)$ of order twenty-eight from a general continued fraction identity of Ramanujan. We establish some theta-function identities for the continued fractions and derive some colour partition identities as applications. Some vanishing coefficients results arising from the continued fractions are also offered.

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Shraddha Rajkhowa, Nipen Saikia. 2023-05-24. Some Identities of Ramanujan's q-Continued Fractions of Order Fourteen and Twenty-Eight, and Vanishing Coefficients. https://arxiv.org/abs/2305.14988

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