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

Shraddha Rajkhowa; Nipen Saikia

paper

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

arXiv:2305.14988

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.

8 Pages