PreprintCC BY 4.0arXiv
Improved rational approximations to Catalan's constant
Abstract
The works of Rivoal, Zudilin, and Krattenthaler and Nesterenko give an explicit sequence pn/qn (pn,qn∈ ℤ, qn>0) of rational approximations to Catalan's constant G=1−1/32+1/52−1/72+1/92−⋯ satisfying | G−pn/qn| ≤ 1/qn0.52 for sufficiently large n. We build on their works to give an explicit sequence pn/qn (pn,qn∈ ℤ, qn>0) with | G−pn/qn| ≤ 1/qn0.62 for sufficiently large n.
Related
- Infinite Product Formula Involving the Catalan's Constant
- Catalan's constant is irrational
- On two families of period integrals related to Catalan's constant
- Rational Dyck Excursion Counts as Sums of Generalized Fuss-Catalan Products
- Admissible qx+1 Sequences, Semiconvergents, and Rational Catalan Numbers
BibTeX
@misc{eskandari2026improved,
title = {{Improved rational approximations to Catalan's constant}},
author = {Payman Eskandari},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26354},
eprint = {2609.26354},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26354},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Improved rational approximations to Catalan's constant
AU - Payman Eskandari
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26354
UR - https://arxiv.org/abs/2609.26354
AB - The works of Rivoal, Zudilin, and Krattenthaler and Nesterenko give an explicit sequence p_n/q_n (p_n,q_n∈ ℤ, q_n>0) of rational approximations to Catalan's constant G=1−1/3^2+1/5^2−1/7^2+1/9^2−⋯ satisfying | G−p_n/q_n| ≤ 1/q_n^0.52 for sufficiently large n. We build on their works to give an explicit sequence p_n/q_n (p_n,q_n∈ ℤ, q_n>0) with | G−p_n/q_n| ≤ 1/q_n^0.62 for sufficiently large n.
ER -