A Formal Refutation of the Hypergeometric Parametric Extension for Reciprocal Binomial Sums
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915921792073728 |
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| author | Ashfaque, Johar M. |
| author_facet | Ashfaque, Johar M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06295 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Formal Refutation of the Hypergeometric Parametric Extension for Reciprocal Binomial Sums Ashfaque, Johar M. Combinatorics 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. |
| title | A Formal Refutation of the Hypergeometric Parametric Extension for Reciprocal Binomial Sums |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2604.06295 |