{"paper":{"title":"Computation of a numerically satisfactory pair of solutions of the differential equation for conical functions of non-negative integer orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.CA","authors_text":"A. Gil, J. Segura, N. M. Temme, T. M. Dunster","submitted_at":"2014-03-31T09:38:23Z","abstract_excerpt":"We consider the problem of computing satisfactory pairs of solutions of the differential equation for Legendre functions of non-negative integer order $\\mu$ and degree $-\\frac12+i\\tau$, where $\\tau$ is a non-negative real parameter. Solutions of this equation are the conical functions ${\\rm{P}}^{\\mu}_{-\\frac12+i\\tau}(x)$ and ${Q}^{\\mu}_{-\\frac12+i\\tau}(x)$, $x>-1$. An algorithm for computing a numerically satisfactory pair of solutions is already available when $-1<x<1$ (see \\cite{gil:2009:con}, \\cite{gil:2012:cpc}).In this paper, we present a stable computational scheme for a real valued nume"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7927","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"}