{"paper":{"title":"On a Class of Hypergeometric Sums via Recurrences and Product Binomial-Harmonic Identities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NT","authors_text":"Narendra Bhandari","submitted_at":"2026-07-11T05:49:28Z","abstract_excerpt":"We study hypergeometric series with coefficients \\(\n  a_n(\\alpha)=\\frac{(\\alpha)_n(1-\\alpha)_n}{(n!)^2},\\) where \\(0< \\alpha < 1\\). The main idea is to introduce a shift parameter in the linear denominator and consider \\[\n  \\Phi_{m,\\varepsilon}(\\lambda;\\alpha)\n  =\n  \\sum_{n=0}^{\\infty}\\varepsilon^n\n  \\frac{a_n(\\alpha)}{n+m+1+\\lambda},\n  \\qquad \\varepsilon\\in\\{1,-1\\}. \\] Expanding this expression in powers of \\(\\lambda\\) produces sums with denominator powers \\((n+m+1)^{-K}\\). We first discuss analytic interpolation in the denominator exponent and explain why positive integer exponents lead to t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10135","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.10135/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}