English

Ramanujan's $q$-continued fractions

Classical Analysis and ODEs 2022-08-29 v1 Number Theory

Abstract

Ramanujan's qq-continued fractions are a central part of Ramanujan's development of basic hypergeometric series. They appear in Chapter 16 of Part III and Chapter 32 of Part V of {\em Ramanujan's Notebooks} edited by Berndt, and in Volume I of Andrews and Berndt's {\em Ramanujan's Lost Notebook}. In these references the continued fractions as presented in the order in which they appear in Ramanujan's original notebooks. We summarize the work of several authors on this topic and re-organize Ramanujan's qq-continued fractions.

Keywords

Cite

@article{arxiv.2208.12656,
  title  = {Ramanujan's $q$-continued fractions},
  author = {Gaurav Bhatnagar},
  journal= {arXiv preprint arXiv:2208.12656},
  year   = {2022}
}

Comments

15 pages. Feedback is invited

R2 v1 2026-06-25T02:00:21.262Z