Variations on a theme of Ap\'ery
Number Theory
2025-11-04 v3 Classical Analysis and ODEs
Combinatorics
Abstract
Ap\'ery's remarkable discovery of rapidly converging continued fractions with small coefficients for and has led to a flurry of important activity in an incredible variety of different directions. Our purpose is to show that modifications of Ap\'ery's continued fractions can give interesting results including new rapidly convergent continued fractions for certain interesting constants.
Cite
@article{arxiv.2501.10090,
title = {Variations on a theme of Ap\'ery},
author = {Henri Cohen and Wadim Zudilin},
journal= {arXiv preprint arXiv:2501.10090},
year = {2025}
}
Comments
16 pages