{"paper":{"title":"Conical: an extended module for computing a numerically satisfactory pair of solutions of the differential equation for conical functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"cs.MS","authors_text":"A. Gil, J. Segura, N. M. Temme, T. M. Dunster","submitted_at":"2017-04-04T18:28:01Z","abstract_excerpt":"Conical functions appear in a large number of applications in physics and engineering. In this paper we describe an extension of our module CONICAL for the computation of conical functions. Specifically, the module includes now a routine for computing the function ${{\\rm R}}^{m}_{-\\frac{1}{2}+i\\tau}(x)$, a real-valued numerically satisfactory companion of the function ${\\rm P}^m_{-\\tfrac12+i\\tau}(x)$ for $x>1$. In this way, a natural basis for solving Dirichlet problems bounded by conical domains is provided."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01145","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"}