{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T22:08:20Z","timestamp":1766786900298,"version":"3.41.0"},"reference-count":15,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2013,2,1]],"date-time":"2013-02-01T00:00:00Z","timestamp":1359676800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[2013,2]]},"abstract":"<jats:p>\n            An algorithm for accurately computing the lower incomplete gamma function\n            <jats:italic>\u03b3<\/jats:italic>\n            (\n            <jats:italic>a<\/jats:italic>\n            ,\n            <jats:italic>t<\/jats:italic>\n            ) in the case where\n            <jats:italic>a<\/jats:italic>\n            =\n            <jats:italic>n<\/jats:italic>\n            + 1\/2,\n            <jats:italic>n<\/jats:italic>\n            \u2208 Z and\n            <jats:italic>t<\/jats:italic>\n            &lt; 0 is described. Series expansions and analytic continuation are employed to compute the function for certain critical values of\n            <jats:italic>n<\/jats:italic>\n            , and these results are used to initiate stable recurrence. The algorithm has been implemented in Fortran 2003, with precompuations carried out in Maple.\n          <\/jats:p>","DOI":"10.1145\/2427023.2427031","type":"journal-article","created":{"date-parts":[[2013,2,22]],"date-time":"2013-02-22T19:25:04Z","timestamp":1361561104000},"page":"1-9","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":6,"title":["Algorithm 926"],"prefix":"10.1145","volume":"39","author":[{"given":"Ian","family":"Thompson","sequence":"first","affiliation":[{"name":"University of Liverpool"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2013,2]]},"reference":[{"key":"e_1_2_2_1_1","unstructured":"Abramowitz M. and Stegun I. A. 1965. Handbook of Mathematical Functions. Dover Publications New York.   Abramowitz M. and Stegun I. A. 1965. Handbook of Mathematical Functions . Dover Publications New York."},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/355900.355908"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/78928.78934"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/78928.78933"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/355853.355863"},{"volume-title":"Tricomi\u2019s Ideas and Contemporary Applied Mathematics. Number 147 in Atti dei Convegni Lincei. Roma : Accademia nazionale dei Lincel","author":"Gautschi W.","key":"e_1_2_2_6_1"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/305658.305717"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/103162.103163"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1023\/B:JOMC.0000044521.18885.d3"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1137\/09075130X"},{"key":"e_1_2_2_11_1","unstructured":"Olver F. W. J. Lozier D. W. Boisvert R. F. and Clark C. W. 2010. NIST Handbook of Mathematical Functions. Cambridge University Press.   Olver F. W. J. Lozier D. W. Boisvert R. F. and Clark C. W. 2010. NIST Handbook of Mathematical Functions . Cambridge University Press."},{"key":"e_1_2_2_12_1","unstructured":"Sterbenz P. H. 1974. Floating-Point Computation. Prentice--Hall.  Sterbenz P. H. 1974. Floating-Point Computation . Prentice--Hall."},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1080\/10652469.2011.597391"},{"key":"e_1_2_2_14_1","unstructured":"Wimp J. 1984. Computation with Recurrence Relations. Pitman Lonodon.  Wimp J. 1984. Computation with Recurrence Relations . Pitman Lonodon."},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.5555\/1756748.1756840"}],"container-title":["ACM Transactions on Mathematical Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2427023.2427031","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2427023.2427031","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T08:49:00Z","timestamp":1750236540000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2427023.2427031"}},"subtitle":["Incomplete Gamma Functions with Negative Arguments"],"short-title":[],"issued":{"date-parts":[[2013,2]]},"references-count":15,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2013,2]]}},"alternative-id":["10.1145\/2427023.2427031"],"URL":"https:\/\/doi.org\/10.1145\/2427023.2427031","relation":{},"ISSN":["0098-3500","1557-7295"],"issn-type":[{"type":"print","value":"0098-3500"},{"type":"electronic","value":"1557-7295"}],"subject":[],"published":{"date-parts":[[2013,2]]},"assertion":[{"value":"2011-08-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-06-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2013-02-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}