English

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 ζ(2)\zeta(2) and ζ(3)\zeta(3) 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.

Keywords

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

R2 v1 2026-06-28T21:09:10.182Z