{"paper":{"title":"Orthogonal polynomials with the Prudnikov-type weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Semyon Yakubovich","submitted_at":"2019-02-17T09:07:54Z","abstract_excerpt":"New sequences of orthogonal polynomials with respect to the weight functions $e^{-x} \\rho_\\nu(x),\\ e^{- 1/x} x^{-1} \\rho_{\\nu} (x), \\rho_{\\nu}(x)= 2 x^{\\nu/2} K_\\nu(2\\sqrt x),\\ x >0, \\nu \\in \\mathbb{R}$, where $K_\\nu(z)$ is the modified Bessel function, are investigated. The recurrence relations, explicit representations, generating functions and Rodrigues-type formulae are obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06227","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"}