PreprintCC BY 4.0arXiv
On series involving binom4kk−1
Abstract
In this article, we prove two conjectures of Sun concerning the evaluation of two series involving the reciprocal of the binomial coefficient binom4kk. The values of these series are related to π, log3, and the Gieseking constant Cl2(π/3). Our proofs rely on the Beta function and the Clausen function.
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BibTeX
@misc{lan2026series,
title = {{On series involving $\binom4kk^-1$}},
author = {Roman Le Lan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22304},
eprint = {2609.22304},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22304},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On series involving binom4kk^−1
AU - Roman Le Lan
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.22304
UR - https://arxiv.org/abs/2609.22304
AB - In this article, we prove two conjectures of Sun concerning the evaluation of two series involving the reciprocal of the binomial coefficient binom4kk. The values of these series are related to π, log3, and the Gieseking constant Cl_2(π/3). Our proofs rely on the Beta function and the Clausen function.
ER -