{"id":"https://openalex.org/W3208171057","doi":"https://doi.org/10.3390/axioms10040279","title":"A Series Representation for the Hurwitz\u2013Lerch Zeta Function","display_name":"A Series Representation for the Hurwitz\u2013Lerch Zeta Function","publication_year":2021,"publication_date":"2021-10-28","ids":{"openalex":"https://openalex.org/W3208171057","doi":"https://doi.org/10.3390/axioms10040279","mag":"3208171057"},"language":"en","primary_location":{"id":"doi:10.3390/axioms10040279","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10040279","pdf_url":"https://www.mdpi.com/2075-1680/10/4/279/pdf?version=1635409773","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/10/4/279/pdf?version=1635409773","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":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.21493382,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":"4","first_page":"279","last_page":"279"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9984999895095825,"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":0.9984999895095825,"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":0.9951000213623047,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9904999732971191,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5912434458732605},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5318588614463806},{"id":"https://openalex.org/keywords/digamma-function","display_name":"Digamma function","score":0.5209685564041138},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.517846405506134},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.49625879526138306},{"id":"https://openalex.org/keywords/gamma-function","display_name":"Gamma function","score":0.49281981587409973},{"id":"https://openalex.org/keywords/riemann-zeta-function","display_name":"Riemann zeta function","score":0.44821232557296753},{"id":"https://openalex.org/keywords/incomplete-gamma-function","display_name":"Incomplete gamma function","score":0.4393608868122101},{"id":"https://openalex.org/keywords/arithmetic-zeta-function","display_name":"Arithmetic zeta function","score":0.26464182138442993},{"id":"https://openalex.org/keywords/prime-zeta-function","display_name":"Prime zeta function","score":0.23330506682395935}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5912434458732605},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5318588614463806},{"id":"https://openalex.org/C30573924","wikidata":"https://www.wikidata.org/wiki/Q905326","display_name":"Digamma function","level":5,"score":0.5209685564041138},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.517846405506134},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.49625879526138306},{"id":"https://openalex.org/C82240120","wikidata":"https://www.wikidata.org/wiki/Q190573","display_name":"Gamma function","level":2,"score":0.49281981587409973},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.44821232557296753},{"id":"https://openalex.org/C17964538","wikidata":"https://www.wikidata.org/wiki/Q1319246","display_name":"Incomplete gamma function","level":3,"score":0.4393608868122101},{"id":"https://openalex.org/C35861355","wikidata":"https://www.wikidata.org/wiki/Q4791135","display_name":"Arithmetic zeta function","level":3,"score":0.26464182138442993},{"id":"https://openalex.org/C71897612","wikidata":"https://www.wikidata.org/wiki/Q1896470","display_name":"Prime zeta function","level":4,"score":0.23330506682395935},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms10040279","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10040279","pdf_url":"https://www.mdpi.com/2075-1680/10/4/279/pdf?version=1635409773","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:31e9b513b1aa4b918d915f4f7dbcb1de","is_oa":true,"landing_page_url":"https://doaj.org/article/31e9b513b1aa4b918d915f4f7dbcb1de","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":"Axioms, Vol 10, Iss 4, p 279 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/10/4/279/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms10040279","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":"Axioms; Volume 10; Issue 4; Pages: 279","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms10040279","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10040279","pdf_url":"https://www.mdpi.com/2075-1680/10/4/279/pdf?version=1635409773","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.5600000023841858,"display_name":"Reduced inequalities"}],"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":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3208171057.pdf","grobid_xml":"https://content.openalex.org/works/W3208171057.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1985680872","https://openalex.org/W2014315805","https://openalex.org/W3032950749","https://openalex.org/W3047896319","https://openalex.org/W3082024070","https://openalex.org/W3104060427","https://openalex.org/W4234858429","https://openalex.org/W4243872063"],"related_works":["https://openalex.org/W2320682263","https://openalex.org/W3021136872","https://openalex.org/W4281872105","https://openalex.org/W3195614928","https://openalex.org/W2588504630","https://openalex.org/W2003470946","https://openalex.org/W2373883749","https://openalex.org/W2160816886","https://openalex.org/W2086639589","https://openalex.org/W2036459900"],"abstract_inverted_index":{"We":[0],"derive":[1],"a":[2],"new":[3],"formula":[4],"for":[5],"the":[6,13,17],"Hurwitz\u2013Lerch":[7],"zeta":[8],"function":[9],"in":[10,25],"terms":[11,26],"of":[12,16,27],"infinite":[14],"sum":[15],"incomplete":[18],"gamma":[19],"function.":[20],"Special":[21],"cases":[22],"are":[23],"derived":[24],"fundamental":[28],"constants.":[29]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
