{"id":"https://openalex.org/W4200452414","doi":"https://doi.org/10.3390/sym13122369","title":"A Note on the Summation of the Incomplete Gamma Function","display_name":"A Note on the Summation of the Incomplete Gamma Function","publication_year":2021,"publication_date":"2021-12-09","ids":{"openalex":"https://openalex.org/W4200452414","doi":"https://doi.org/10.3390/sym13122369"},"language":"en","primary_location":{"id":"doi:10.3390/sym13122369","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13122369","pdf_url":"https://www.mdpi.com/2073-8994/13/12/2369/pdf?version=1639020558","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/12/2369/pdf?version=1639020558","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087461159","display_name":"Robert Reynolds","orcid":"https://orcid.org/0000-0002-4230-9925"},"institutions":[{"id":"https://openalex.org/I192455969","display_name":"York University","ror":"https://ror.org/05fq50484","country_code":"CA","type":"education","lineage":["https://openalex.org/I192455969"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Robert Reynolds","raw_affiliation_strings":["Department of Mathematics and Statistics, York University, Toronto, ON M3J1P3, Canada"],"raw_orcid":"https://orcid.org/0000-0002-4230-9925","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, York University, Toronto, ON M3J1P3, Canada","institution_ids":["https://openalex.org/I192455969"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071344976","display_name":"A D Stauffer","orcid":"https://orcid.org/0000-0002-7252-5004"},"institutions":[{"id":"https://openalex.org/I192455969","display_name":"York University","ror":"https://ror.org/05fq50484","country_code":"CA","type":"education","lineage":["https://openalex.org/I192455969"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Allan Stauffer","raw_affiliation_strings":["Department of Mathematics and Statistics, York University, Toronto, ON M3J1P3, Canada"],"raw_orcid":"https://orcid.org/0000-0002-7252-5004","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, York University, Toronto, ON M3J1P3, Canada","institution_ids":["https://openalex.org/I192455969"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5087461159"],"corresponding_institution_ids":["https://openalex.org/I192455969"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.6509,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.84131348,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"13","issue":"12","first_page":"2369","last_page":"2369"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11822","display_name":"Analytic and geometric function theory","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6004313826560974},{"id":"https://openalex.org/keywords/gamma-function","display_name":"Gamma function","score":0.5751059055328369},{"id":"https://openalex.org/keywords/incomplete-gamma-function","display_name":"Incomplete gamma function","score":0.48227646946907043},{"id":"https://openalex.org/keywords/riemann-zeta-function","display_name":"Riemann zeta function","score":0.47496578097343445},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.47428756952285767},{"id":"https://openalex.org/keywords/table","display_name":"Table (database)","score":0.458800733089447},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4546213746070862},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.42874041199684143},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26650115847587585},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17903786897659302}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6004313826560974},{"id":"https://openalex.org/C82240120","wikidata":"https://www.wikidata.org/wiki/Q190573","display_name":"Gamma function","level":2,"score":0.5751059055328369},{"id":"https://openalex.org/C17964538","wikidata":"https://www.wikidata.org/wiki/Q1319246","display_name":"Incomplete gamma function","level":3,"score":0.48227646946907043},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.47496578097343445},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.47428756952285767},{"id":"https://openalex.org/C45235069","wikidata":"https://www.wikidata.org/wiki/Q278425","display_name":"Table (database)","level":2,"score":0.458800733089447},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4546213746070862},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42874041199684143},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26650115847587585},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17903786897659302},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13122369","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13122369","pdf_url":"https://www.mdpi.com/2073-8994/13/12/2369/pdf?version=1639020558","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:3b78184908d54e30996d442c4dab3a3b","is_oa":true,"landing_page_url":"https://doaj.org/article/3b78184908d54e30996d442c4dab3a3b","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 12, p 2369 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/12/2369/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13122369","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13122369","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13122369","pdf_url":"https://www.mdpi.com/2073-8994/13/12/2369/pdf?version=1639020558","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education","score":0.8600000143051147}],"awards":[{"id":"https://openalex.org/G2993406232","display_name":null,"funder_award_id":"504070","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4200452414.pdf"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1985857248","https://openalex.org/W2014315805","https://openalex.org/W2985260182","https://openalex.org/W3011860698","https://openalex.org/W3032950749","https://openalex.org/W3043482616","https://openalex.org/W3047896319","https://openalex.org/W3203636883","https://openalex.org/W4234858429"],"related_works":["https://openalex.org/W3195614928","https://openalex.org/W2951910363","https://openalex.org/W2151817761","https://openalex.org/W4299284825","https://openalex.org/W2611222790","https://openalex.org/W2003470946","https://openalex.org/W2373883749","https://openalex.org/W2086639589","https://openalex.org/W2036459900","https://openalex.org/W2160816886"],"abstract_inverted_index":{"We":[0,18],"examine":[1],"the":[2,7,15,21],"improved":[3],"infinite":[4,22],"sum":[5,23],"of":[6,14,36],"incomplete":[8],"gamma":[9],"function":[10,28],"for":[11,38],"large":[12],"values":[13,31],"parameters":[16],"involved.":[17],"also":[19],"evaluate":[20],"and":[24,32],"equivalent":[25],"Hurwitz-Lerch":[26,43],"zeta":[27,44],"at":[29],"special":[30],"produce":[33],"a":[34],"table":[35],"results":[37],"easy":[39],"reading.":[40],"Almost":[41],"all":[42],"functions":[45],"have":[46],"an":[47],"asymmetrical":[48],"zero":[49],"distribution.":[50]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
