{"id":"https://openalex.org/W4289529481","doi":"https://doi.org/10.3390/sym14081573","title":"Non-Zero Order of an Extended Temme Integral","display_name":"Non-Zero Order of an Extended Temme Integral","publication_year":2022,"publication_date":"2022-07-30","ids":{"openalex":"https://openalex.org/W4289529481","doi":"https://doi.org/10.3390/sym14081573"},"language":"en","primary_location":{"id":"doi:10.3390/sym14081573","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14081573","pdf_url":"https://www.mdpi.com/2073-8994/14/8/1573/pdf?version=1661237738","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/2073-8994/14/8/1573/pdf?version=1661237738","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 M3J 1P3, Canada"],"raw_orcid":"https://orcid.org/0000-0002-4230-9925","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, 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 M3J 1P3, Canada"],"raw_orcid":"https://orcid.org/0000-0002-7252-5004","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, 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":0.3556,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.49057295,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"14","issue":"8","first_page":"1573","last_page":"1573"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.998199999332428,"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":0.998199999332428,"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9919999837875366,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polylogarithm","display_name":"Polylogarithm","score":0.8606205582618713},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7137280702590942},{"id":"https://openalex.org/keywords/riemann-zeta-function","display_name":"Riemann zeta function","score":0.6445614099502563},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.621549665927887},{"id":"https://openalex.org/keywords/bessel-function","display_name":"Bessel function","score":0.5618912577629089},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5163818597793579},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.48993080854415894},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.44672828912734985},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4309636354446411},{"id":"https://openalex.org/keywords/prime-zeta-function","display_name":"Prime zeta function","score":0.35030853748321533},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3359261155128479},{"id":"https://openalex.org/keywords/arithmetic-zeta-function","display_name":"Arithmetic zeta function","score":0.3220973014831543}],"concepts":[{"id":"https://openalex.org/C186934003","wikidata":"https://www.wikidata.org/wiki/Q1238449","display_name":"Polylogarithm","level":5,"score":0.8606205582618713},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7137280702590942},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.6445614099502563},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.621549665927887},{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.5618912577629089},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5163818597793579},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48993080854415894},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.44672828912734985},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4309636354446411},{"id":"https://openalex.org/C71897612","wikidata":"https://www.wikidata.org/wiki/Q1896470","display_name":"Prime zeta function","level":4,"score":0.35030853748321533},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3359261155128479},{"id":"https://openalex.org/C35861355","wikidata":"https://www.wikidata.org/wiki/Q4791135","display_name":"Arithmetic zeta function","level":3,"score":0.3220973014831543},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14081573","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14081573","pdf_url":"https://www.mdpi.com/2073-8994/14/8/1573/pdf?version=1661237738","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:28c6e3f86dc3428b87a2c2bc05a3e106","is_oa":true,"landing_page_url":"https://doaj.org/article/28c6e3f86dc3428b87a2c2bc05a3e106","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 14, Iss 8, p 1573 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/8/1573/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14081573","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/sym14081573","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14081573","pdf_url":"https://www.mdpi.com/2073-8994/14/8/1573/pdf?version=1661237738","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":[],"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":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4289529481.pdf"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W2896308741","https://openalex.org/W3032950749","https://openalex.org/W3047896319","https://openalex.org/W4232669643","https://openalex.org/W4233086413","https://openalex.org/W4234858429"],"related_works":["https://openalex.org/W68100126","https://openalex.org/W2186103008","https://openalex.org/W3124095481","https://openalex.org/W4297785894","https://openalex.org/W2106729030","https://openalex.org/W4300263998","https://openalex.org/W4297814030","https://openalex.org/W3216251873","https://openalex.org/W2092735642","https://openalex.org/W2963858425"],"abstract_inverted_index":{"A":[0,42],"new":[1],"three-dimensional":[2],"integral":[3,21,31,63],"containing":[4],"f(x,y,z)Iv(x\u03b1)":[5],"is":[6,10,22,32],"derived":[7],"where":[8],"Iv(x\u03b1)":[9],"the":[11,16,20,25,40,47],"Modified":[12],"Bessel":[13],"Function":[14],"of":[15,39,46,67],"first":[17],"kind":[18],"and":[19,53],"taken":[23],"over":[24],"infinite":[26],"cubic":[27],"space":[28],"0&lt;x&lt;\u221e,0&lt;y&lt;\u221e,0&lt;z&lt;\u221e.":[29],"The":[30],"not":[33],"easily":[34],"evaluated":[35],"for":[36],"complex":[37],"ranges":[38],"parameters.":[41],"representation":[43,60],"in":[44,65],"terms":[45,66],"Hurwitz\u2013Lerch":[48],"zeta":[49,55],"function,":[50],"polylogarithm":[51],"function":[52],"Riemann":[54],"functions":[56,77],"are":[57],"evaluated.":[58],"This":[59],"yields":[61],"triple":[62],"representations":[64],"fundamental":[68],"constants":[69],"that":[70],"can":[71],"be":[72],"derived.":[73],"Almost":[74],"all":[75],"Lerch":[76],"have":[78],"an":[79],"asymmetrical":[80],"zero":[81],"distribution.":[82]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
