A formula for the convergents of a continued fraction of Ramanujan

2016/03/24 by Gaurav Bhatnagar, Bhatnagar, Gaurav, Michael D. Hirschhorn +1
Mathematics · #33D15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1603.07664

openalex publication_date 2016/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In Entry 16, Chapter 16 of his notebooks, Ramanujan himself gave a formula for the convergents of the famous Rogers-Ramanujan continued fraction. We provide a similar formula for the convergents of a more general continued fraction, namely Entry 15 of Chapter 16.

Related

• The Rogers--Ramanujan continued fraction
• Notes On a Continued Fraction of Ramanujan
• Generalizations of Ramanujans Continued fractions
• Ramanujan's q-continued fractions
• Properties of reciprocity formulas for the Rogers-Ramanujan continued fractions