Bruce Berndt ; Victoria Reuter - Continued Fractions in Entries 34 and 25 of Chapter 12 in Ramanujan's Second Notebook

hrj:17899 - Hardy-Ramanujan Journal, April 27, 2026, Volume 48 - 2025 - https://doi.org/10.46298/hrj.2026.17899
Continued Fractions in Entries 34 and 25 of Chapter 12 in Ramanujan's Second NotebookArticle

Authors: Bruce Berndt 1; Victoria Reuter


Chapter 12 in Ramanujan's second notebook is devoted to continued fractions, many of which are evaluated in terms of Gamma functions. Using the theory of hypergeometric functions, we give new proofs of two of the most attractive continued fractions, and also two new companions.

https://doi.org/10.46298/hrj.2026.17899
Source: HAL:hal-05562868v1
Volume: Volume 48 - 2025
Published on: April 27, 2026
Accepted on: April 27, 2026
Submitted on: April 2, 2026
Keywords: 11A55; 33C20, 33C90, [MATH]Mathematics [math], [en] Ramanujan's notebooks., hypergeometric functions, continued fractions
Licence: Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)

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