{"paper":{"title":"Computation of the incomplete gamma function for negative values of the argument","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"cs.MS","authors_text":"A. Gil, D. Ruiz-Antol\\'in, J. Segura, N. M. Temme","submitted_at":"2016-08-14T23:17:03Z","abstract_excerpt":"An algorithm for computing the incomplete gamma function $\\gamma^*(a,z)$ for real values of the parameter $a$ and negative real values of the argument $z$ is presented. The algorithm combines the use of series expansions, Poincar\\'e-type expansions, uniform asymptotic expansions and recurrence relations, depending on the parameter region. A relative accuracy $\\sim 10^{-13}$ in the parameter region $(a,z) \\in [-500,\\,500] \\times [-500,\\,0)$ can be obtained when computing the function $\\gamma^*(a,z)$ with the Fortran 90 module IncgamNEG implementing the algorithm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04152","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"}