{"paper":{"title":"On generating functions and Mehler--Heine formulas for discrete Charlier and Meixner Sobolev-type orthogonal polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Anier Soria Lorente, Junior Michel","submitted_at":"2026-07-14T15:32:54Z","abstract_excerpt":"Generating functions are among the most important analytical tools in the theory of orthogonal polynomials, providing a unified framework for deriving structural identities, asymptotic expansions, and zero distributions. However, despite the extensive development of discrete Sobolev orthogonal polynomials, no general generating-function theory has been available for the Sobolev-type Charlier and Meixner families associated with arbitrary-order forward differences $j\\geq 1$ and an exterior mass point $\\alpha<0$. In this paper, we develop the first unified generating-function framework for these"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.12889","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/2607.12889/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"}