{"id":"https://openalex.org/W3206134081","doi":"https://doi.org/10.3390/sym13111983","title":"A Double Logarithmic Transform Involving the Exponential and Polynomial Functions Expressed in Terms of the Hurwitz\u2013Lerch Zeta Function","display_name":"A Double Logarithmic Transform Involving the Exponential and Polynomial Functions Expressed in Terms of the Hurwitz\u2013Lerch Zeta Function","publication_year":2021,"publication_date":"2021-10-20","ids":{"openalex":"https://openalex.org/W3206134081","doi":"https://doi.org/10.3390/sym13111983","mag":"3206134081"},"language":"en","primary_location":{"id":"doi:10.3390/sym13111983","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13111983","pdf_url":"https://www.mdpi.com/2073-8994/13/11/1983/pdf?version=1635840922","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/2073-8994/13/11/1983/pdf?version=1635840922","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":0.6603,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.65960957,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"13","issue":"11","first_page":"1983","last_page":"1983"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9958999752998352,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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":0.6711403727531433},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6101556420326233},{"id":"https://openalex.org/keywords/bernoulli-polynomials","display_name":"Bernoulli polynomials","score":0.5671911239624023},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5396459698677063},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4735364615917206},{"id":"https://openalex.org/keywords/logarithmic-derivative","display_name":"Logarithmic derivative","score":0.43080857396125793},{"id":"https://openalex.org/keywords/riemann-zeta-function","display_name":"Riemann zeta function","score":0.41356945037841797},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3701644837856293}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6711403727531433},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6101556420326233},{"id":"https://openalex.org/C196172290","wikidata":"https://www.wikidata.org/wiki/Q2346201","display_name":"Bernoulli polynomials","level":4,"score":0.5671911239624023},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5396459698677063},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4735364615917206},{"id":"https://openalex.org/C36649600","wikidata":"https://www.wikidata.org/wiki/Q762521","display_name":"Logarithmic derivative","level":2,"score":0.43080857396125793},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.41356945037841797},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3701644837856293},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.0},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13111983","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13111983","pdf_url":"https://www.mdpi.com/2073-8994/13/11/1983/pdf?version=1635840922","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:923024447c5a48aa90e76dfd9ae7a813","is_oa":true,"landing_page_url":"https://doaj.org/article/923024447c5a48aa90e76dfd9ae7a813","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 11, p 1983 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/11/1983/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13111983","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/sym13111983","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13111983","pdf_url":"https://www.mdpi.com/2073-8994/13/11/1983/pdf?version=1635840922","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/W3206134081.pdf"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1659874285","https://openalex.org/W1982907413","https://openalex.org/W2044550654","https://openalex.org/W2765439416","https://openalex.org/W2929379250","https://openalex.org/W2995812194","https://openalex.org/W3032950749","https://openalex.org/W3047896319","https://openalex.org/W3100475825","https://openalex.org/W4234858429","https://openalex.org/W4241654653","https://openalex.org/W6771593766"],"related_works":["https://openalex.org/W3100954504","https://openalex.org/W2499297376","https://openalex.org/W3022449129","https://openalex.org/W1588317520","https://openalex.org/W2606781077","https://openalex.org/W4386731851","https://openalex.org/W125268981","https://openalex.org/W1519862060","https://openalex.org/W2490289125","https://openalex.org/W4308335832"],"abstract_inverted_index":{"The":[0],"object":[1],"of":[2,13,33],"this":[3,40],"paper":[4],"is":[5],"to":[6],"derive":[7],"a":[8],"double":[9],"integral":[10],"in":[11,31,39],"terms":[12,32],"the":[14,37],"Hurwitz\u2013Lerch":[15,20],"zeta":[16,21],"function.":[17],"Almost":[18],"all":[19],"functions":[22],"have":[23],"an":[24],"asymmetrical":[25],"zero-distribution.":[26],"Special":[27],"cases":[28],"are":[29,42],"evaluated":[30],"fundamental":[34],"constants.":[35],"All":[36],"results":[38],"work":[41],"new.":[43]},"counts_by_year":[{"year":2022,"cited_by_count":2}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
