{"id":"https://openalex.org/W4200612513","doi":"https://doi.org/10.3390/sym14010009","title":"A Quadruple Integral Involving Product of the Struve Hv(\u03b2t) and Parabolic Cylinder Du(\u03b1x) Functions","display_name":"A Quadruple Integral Involving Product of the Struve Hv(\u03b2t) and Parabolic Cylinder Du(\u03b1x) Functions","publication_year":2021,"publication_date":"2021-12-22","ids":{"openalex":"https://openalex.org/W4200612513","doi":"https://doi.org/10.3390/sym14010009"},"language":"en","primary_location":{"id":"doi:10.3390/sym14010009","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14010009","pdf_url":"https://www.mdpi.com/2073-8994/14/1/9/pdf?version=1640232520","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/2073-8994/14/1/9/pdf?version=1640232520","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":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.2589654,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"1","first_page":"9","last_page":"9"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9987999796867371,"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":0.9987999796867371,"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":0.9944000244140625,"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":0.9768000245094299,"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":0.7617325782775879},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5761817693710327},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5376943349838257},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5308875441551208},{"id":"https://openalex.org/keywords/struve-function","display_name":"Struve function","score":0.5211750864982605},{"id":"https://openalex.org/keywords/cylinder","display_name":"Cylinder","score":0.5127469301223755},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.44089072942733765},{"id":"https://openalex.org/keywords/riemann-zeta-function","display_name":"Riemann zeta function","score":0.4401616156101227},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41014358401298523},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.100881427526474}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7617325782775879},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5761817693710327},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5376943349838257},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5308875441551208},{"id":"https://openalex.org/C125065441","wikidata":"https://www.wikidata.org/wiki/Q2607374","display_name":"Struve function","level":5,"score":0.5211750864982605},{"id":"https://openalex.org/C203311528","wikidata":"https://www.wikidata.org/wiki/Q34132","display_name":"Cylinder","level":2,"score":0.5127469301223755},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44089072942733765},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.4401616156101227},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41014358401298523},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.100881427526474},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"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/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14010009","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14010009","pdf_url":"https://www.mdpi.com/2073-8994/14/1/9/pdf?version=1640232520","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:ce73486247c7402abc9664f5b71ab163","is_oa":true,"landing_page_url":"https://doaj.org/article/ce73486247c7402abc9664f5b71ab163","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 1, p 9 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/1/9/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14010009","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/sym14010009","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14010009","pdf_url":"https://www.mdpi.com/2073-8994/14/1/9/pdf?version=1640232520","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/W4200612513.pdf"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W656201571","https://openalex.org/W2023783306","https://openalex.org/W2087107099","https://openalex.org/W2896308741","https://openalex.org/W3032950749","https://openalex.org/W3047896319","https://openalex.org/W4234858429"],"related_works":["https://openalex.org/W2163413354","https://openalex.org/W3129872890","https://openalex.org/W1521003599","https://openalex.org/W4205547735","https://openalex.org/W4293765127","https://openalex.org/W2565874992","https://openalex.org/W2264315092","https://openalex.org/W2031690159","https://openalex.org/W2770834742","https://openalex.org/W2792679725"],"abstract_inverted_index":{"The":[0],"objective":[1],"of":[2,18,30],"the":[3,16,19,31,57,60],"present":[4],"paper":[5],"is":[6],"to":[7],"obtain":[8],"a":[9],"quadruple":[10],"infinite":[11],"integral.":[12],"This":[13],"integral":[14],"involves":[15],"product":[17],"Struve":[20],"and":[21,25,50],"parabolic":[22],"cylinder":[23],"functions":[24,39,53],"expresses":[26],"it":[27],"in":[28,46,59],"terms":[29,47],"Hurwitz\u2013Lerch":[32],"Zeta":[33,38],"function.":[34],"Almost":[35],"all":[36],"Hurwitz-Lerch":[37],"have":[40],"an":[41],"asymmetrical":[42],"zero":[43],"distributionSpecial":[44],"cases":[45],"fundamental":[48],"constants":[49],"other":[51],"special":[52],"are":[54,62],"produced.":[55],"All":[56],"results":[58],"work":[61],"new.":[63]},"counts_by_year":[],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2021-12-31T00:00:00"}