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

2020/05/10 by S. Chandankumar, Chandankumar, S., B. Hemanthkumar +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2005.04595

openalex publication_date 2020/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 φ(q) and ψ(-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.

Citations

• On Ramanujan's cubic continued fraction and explicit evaluations of theta-functions

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• A remark on modular equations involving Rogers-Ramanujan continued fraction via 5-dissections
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