{"paper":{"title":"Appell Polynomials in Shifted Asymptotic Expansions: the Mills ratio, Hermite polynomials, and Stieltjes bounds","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Lenka Mihokovi\\'c, Neven Elezovi\\'c, Tomislav Buri\\'c","submitted_at":"2026-07-29T08:58:27Z","abstract_excerpt":"A theorem of Buri\\'c, Elezovi\\'c and Vuk\\v si\\'c states that translating the argument in an asymptotic expansion, $f(x)\\sim\\sum(-1)^na_nx^{-n-1}$, to $f(x+t)$, replaces the constant coefficients $a_n$ by the Appell polynomials $R_n(t)$ generated by $(a_n)$. Their motivating examples came from the gamma and polygamma functions, where Bernoulli polynomials occur. We extend this construction beyond that setting and identify the Borel--Laplace representation $L_A(x)=\\int_0^\\infty e^{-xs}A(-s)\\,\\dd s$, whenever the integral exists. For the Gaussian kernel $A(-s)=e^{-s^2/2}$, this representation giv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.26636","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/2607.26636/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"}