English

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

Number Theory 2020-05-12 v1

Abstract

Ramanujan in his second notebook recorded total of seven PP--QQ modular equations involving theta--function f(q)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 φ(q)\varphi(q) and ψ(q)\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.

Keywords

Cite

@article{arxiv.2005.04595,
  title  = {$P$--$Q$ "mixed" modular equations of degree 15},
  author = {S. Chandankumar and B. Hemanthkumar},
  journal= {arXiv preprint arXiv:2005.04595},
  year   = {2020}
}
R2 v1 2026-06-23T15:25:55.524Z