On some P-Q mixed modular equations of degree 5

Published 25 Jun 2019 in math.NT | (1907.01634v2)

Abstract: In his second notebook, Ramanujan recorded total of 23 P-Q modular equations involving theta-functions $f(-q)$, $\varphi(q)$ and $\psi(q)$. In this paper, modular equations analogous to those recorded by Ramanujan are obtained involving $f(-q)$. As a consequence, values of certain quotients of theta-function are evaluated.

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