{"paper":{"title":"On the zeros of the Hahn-Exton q-Bessel function and associated q-Lommel polynomials","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Erik Koelink, Ren\\'e F. Swarttouw","submitted_at":"1997-03-03T00:00:00Z","abstract_excerpt":"For the Bessel function \\begin{equation} \\label{bessel} J_{\\nu}(z) = \\sum\\limits_{k=0}^{\\infty} \\frac{(-1)^k \\left( \\frac{z}{2} \\right)^{\\nu+2k}}{k! \\Gamma(\\nu+1+k)} \\end{equation} there exist several $q$-analogues. The oldest $q$-analogues of the Bessel function were introduced by F. H. Jackson at the beginning of this century, see M. E. H. Ismail \\cite{Is1} for the appropriate references. Another $q$-analogue of the Bessel function has been introduced by W. Hahn in a special case and by H. Exton in full generality, see R. F. Swarttouw \\cite{Sw1} for a historic overview.\n  Here we concentrate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9703215","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":""},"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"}