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arXiv · 2005.04595

$P$--$Q$ "mixed" modular equations of degree 15

S. Chandankumar·B. Hemanthkumar
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Abstract

Ramanujan in his second notebook recorded total of seven $P$--$Q$ modular equations involving theta--function $f(-q)$ with moduli of orders 1, 3, 5 and 15. In this paper, modular equations analogous to those recorded by Ramanujan are obtained involving his theta--functions $\varphi(q)$ and $\psi(-q)$ with moduli of orders 1, 3, 5 and 15. As a consequence, several values of quotients of theta--function and a continued fraction of order 12 are explicitly evaluated.

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S. Chandankumar, B. Hemanthkumar. 2020-05-10. $P$--$Q$ "mixed" modular equations of degree 15. https://arxiv.org/abs/2005.04595

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