{"paper":{"title":"Computing Hypergeometric Solutions of Second Order Linear Differential Equations using Quotients of Formal Solutions and Integral Bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"cs.SC","authors_text":"Erdal Imamoglu, Mark van Hoeij","submitted_at":"2016-06-05T22:41:58Z","abstract_excerpt":"We present two algorithms for computing hypergeometric solutions of second order linear differential operators with rational function coefficients. Our first algorithm searches for solutions of the form \\[ \\exp(\\int r \\, dx)\\cdot{_{2}F_1}(a_1,a_2;b_1;f) \\] where $r,f \\in \\overline{\\mathbb{Q}(x)}$, and $a_1,a_2,b_1 \\in \\mathbb{Q}$. It uses modular reduction and Hensel lifting. Our second algorithm tries to find solutions in the form \\[ \\exp(\\int r \\, dx)\\cdot \\left( r_0 \\cdot{_{2}F_1}(a_1,a_2;b_1;f) + r_1 \\cdot{_{2}F_1}'(a_1,a_2;b_1;f) \\right) \\] where $r_0, r_1 \\in \\overline{\\mathbb{Q}(x)}$, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01576","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"}