PreprintCC BY 4.0arXiv
On two families of period integrals related to Catalan's constant
Abstract
The construction of a mixed motive associated with Catalan's constant G=∑n=0∞ (−1)n/(2n+1)2 in [arXiv:2510.20648] led to a supply of period integrals that evaluate to linear forms in 1 and G. Inside this supply, the boundary of the integration domain leads to a natural 3-parameter family of period integrals. We show that this family is closely related to the family of hypergeometric period integrals considered earlier by Rivoal, Zudilin and Nesterenko.
Related
- Infinite Product Formula Involving the Catalan's Constant
- Catalan's constant is irrational
- Improved rational approximations to Catalan's constant
- A note on a recent claimed proof of the irrationality of Catalan's constant
- Equivalence on exponential families as Hessian manifolds and classification of exponential families of order 1 with constant Hessian sectional curvature
BibTeX
@misc{eskandari2026families,
title = {{On two families of period integrals related to Catalan's constant}},
author = {Payman Eskandari},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26308},
eprint = {2609.26308},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26308},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On two families of period integrals related to Catalan's constant
AU - Payman Eskandari
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26308
UR - https://arxiv.org/abs/2609.26308
AB - The construction of a mixed motive associated with Catalan's constant G=∑_n=0^∞ (−1)^n/(2n+1)^2 in [arXiv:2510.20648] led to a supply of period integrals that evaluate to linear forms in 1 and G. Inside this supply, the boundary of the integration domain leads to a natural 3-parameter family of period integrals. We show that this family is closely related to the family of hypergeometric period integrals considered earlier by Rivoal, Zudilin and Nesterenko.
ER -