{"id":"https://openalex.org/W3198829880","doi":"https://doi.org/10.3390/sym13091638","title":"A Quadruple Definite Integral Expressed in Terms of the Lerch Function","display_name":"A Quadruple Definite Integral Expressed in Terms of the Lerch Function","publication_year":2021,"publication_date":"2021-09-06","ids":{"openalex":"https://openalex.org/W3198829880","doi":"https://doi.org/10.3390/sym13091638","mag":"3198829880"},"language":"en","primary_location":{"id":"doi:10.3390/sym13091638","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13091638","pdf_url":"https://www.mdpi.com/2073-8994/13/9/1638/pdf","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/2073-8994/13/9/1638/pdf","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, 4700 Keele Street, 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, 4700 Keele Street, 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, 4700 Keele Street, 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, 4700 Keele Street, 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":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.18567108,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"13","issue":"9","first_page":"1638","last_page":"1638"},"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":0.9972000122070312,"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":0.9970999956130981,"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":0.6949097514152527},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.48182669281959534},{"id":"https://openalex.org/keywords/exponential-integral","display_name":"Exponential integral","score":0.4306900203227997},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3781457543373108},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2905328869819641},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.1430821418762207},{"id":"https://openalex.org/keywords/line-integral","display_name":"Line integral","score":0.0669465959072113}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6949097514152527},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.48182669281959534},{"id":"https://openalex.org/C53819440","wikidata":"https://www.wikidata.org/wiki/Q1419948","display_name":"Exponential integral","level":4,"score":0.4306900203227997},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3781457543373108},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2905328869819641},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.1430821418762207},{"id":"https://openalex.org/C75023562","wikidata":"https://www.wikidata.org/wiki/Q467699","display_name":"Line integral","level":3,"score":0.0669465959072113}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13091638","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13091638","pdf_url":"https://www.mdpi.com/2073-8994/13/9/1638/pdf","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:da80f654d5db441f95a0294b2b5e4626","is_oa":true,"landing_page_url":"https://doaj.org/article/da80f654d5db441f95a0294b2b5e4626","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 9, p 1638 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/9/1638/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13091638","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/sym13091638","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13091638","pdf_url":"https://www.mdpi.com/2073-8994/13/9/1638/pdf","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":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3198829880.pdf"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W29412332","https://openalex.org/W1612848248","https://openalex.org/W1963617751","https://openalex.org/W2013044915","https://openalex.org/W2057003417","https://openalex.org/W2798267538","https://openalex.org/W3032950749","https://openalex.org/W3047896319","https://openalex.org/W4234858429","https://openalex.org/W4244113179","https://openalex.org/W6601194643"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2911222139","https://openalex.org/W2278288215","https://openalex.org/W1519862060","https://openalex.org/W3023142634","https://openalex.org/W4386732094","https://openalex.org/W1588317520","https://openalex.org/W4293406611"],"abstract_inverted_index":{"A":[0],"quadruple":[1],"integral":[2,22],"involving":[3],"the":[4,15,44],"logarithmic,":[5],"exponential":[6],"and":[7,30],"polynomial":[8],"functions":[9,29,36],"is":[10],"derived":[11],"in":[12,25,46],"terms":[13,26],"of":[14,20,27,43],"Lerch":[16,35],"function.":[17],"Special":[18],"cases":[19],"this":[21,47],"are":[23,49],"evaluated":[24],"special":[28],"fundamental":[31],"constants.":[32],"Almost":[33],"all":[34],"have":[37],"an":[38],"asymmetrical":[39],"zero-distribution.":[40],"The":[41],"majority":[42],"results":[45],"work":[48],"new.":[50]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}