A Formal Refutation of the Hypergeometric Parametric Extension for Reciprocal Binomial Sums
Combinatorics
2026-04-09 v1
Abstract
Recent work by Pain [1] proposed a systematic approach to evaluating binomial sums involving reciprocals of binomial coefficients via Beta integrals. In particular, a parametric extension (Proposition 6.1) was introduced and claimed to admit a closed-form representation in terms of a terminating 2F1 hypergeometric function. Through a combination of internal logical consistency checks, integral derivation analysis, and exact symbolic computation, we definitively prove that this parametric identity is false.
Cite
@article{arxiv.2604.06295,
title = {A Formal Refutation of the Hypergeometric Parametric Extension for Reciprocal Binomial Sums},
author = {Johar M. Ashfaque},
journal= {arXiv preprint arXiv:2604.06295},
year = {2026}
}
Comments
Comment on arXiv:2604.04566