{"id":"https://openalex.org/W4210510713","doi":"https://doi.org/10.3390/sym14020280","title":"j-Dimensional Integral Involving the Logarithmic and Exponential Functions: Derivation and Evaluation","display_name":"j-Dimensional Integral Involving the Logarithmic and Exponential Functions: Derivation and Evaluation","publication_year":2022,"publication_date":"2022-01-29","ids":{"openalex":"https://openalex.org/W4210510713","doi":"https://doi.org/10.3390/sym14020280"},"language":"en","primary_location":{"id":"doi:10.3390/sym14020280","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14020280","pdf_url":"https://www.mdpi.com/2073-8994/14/2/280/pdf?version=1643463731","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/2073-8994/14/2/280/pdf?version=1643463731","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"],"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"],"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":0.01344538,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"2","first_page":"280","last_page":"280"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T13116","display_name":"Heat Transfer and Numerical Methods","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.7788318395614624},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.7523688077926636},{"id":"https://openalex.org/keywords/exponential-integral","display_name":"Exponential integral","score":0.6514893174171448},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6025177836418152},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4855439364910126},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47915762662887573},{"id":"https://openalex.org/keywords/volume-integral","display_name":"Volume integral","score":0.43823009729385376},{"id":"https://openalex.org/keywords/exponential-formula","display_name":"Exponential formula","score":0.4222829043865204},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3824375867843628},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31818073987960815},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2830051779747009},{"id":"https://openalex.org/keywords/double-exponential-function","display_name":"Double exponential function","score":0.2521142363548279},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.23046210408210754},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05375558137893677}],"concepts":[{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.7788318395614624},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.7523688077926636},{"id":"https://openalex.org/C53819440","wikidata":"https://www.wikidata.org/wiki/Q1419948","display_name":"Exponential integral","level":4,"score":0.6514893174171448},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6025177836418152},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4855439364910126},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47915762662887573},{"id":"https://openalex.org/C51577431","wikidata":"https://www.wikidata.org/wiki/Q1788036","display_name":"Volume integral","level":3,"score":0.43823009729385376},{"id":"https://openalex.org/C92867014","wikidata":"https://www.wikidata.org/wiki/Q5421523","display_name":"Exponential formula","level":4,"score":0.4222829043865204},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3824375867843628},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31818073987960815},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2830051779747009},{"id":"https://openalex.org/C49016629","wikidata":"https://www.wikidata.org/wiki/Q3075235","display_name":"Double exponential function","level":3,"score":0.2521142363548279},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.23046210408210754},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05375558137893677},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14020280","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14020280","pdf_url":"https://www.mdpi.com/2073-8994/14/2/280/pdf?version=1643463731","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:7f135068d46047b3a967315005cc641f","is_oa":true,"landing_page_url":"https://doaj.org/article/7f135068d46047b3a967315005cc641f","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 2, p 280 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/2/280/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14020280","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/sym14020280","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14020280","pdf_url":"https://www.mdpi.com/2073-8994/14/2/280/pdf?version=1643463731","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/G3062003504","display_name":null,"funder_award_id":"505070","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/W4210510713.pdf","grobid_xml":"https://content.openalex.org/works/W4210510713.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W656201571","https://openalex.org/W2035925506","https://openalex.org/W2057817591","https://openalex.org/W2321957512","https://openalex.org/W2913829066","https://openalex.org/W3031197895","https://openalex.org/W3032950749","https://openalex.org/W3047896319","https://openalex.org/W3206134081","https://openalex.org/W3212029589","https://openalex.org/W4234858429"],"related_works":["https://openalex.org/W125268981","https://openalex.org/W1986856081","https://openalex.org/W1964066794","https://openalex.org/W2499297376","https://openalex.org/W2606781077","https://openalex.org/W2007983172","https://openalex.org/W4386732094","https://openalex.org/W1552187743","https://openalex.org/W1519862060","https://openalex.org/W1588317520"],"abstract_inverted_index":{"In":[0],"the":[1,40,43,47,52],"fields":[2],"of":[3,20,23,42,46],"science":[4],"and":[5,25],"engineering,":[6],"tasks":[7],"involving":[8],"repeated":[9,18],"integrals":[10,19],"appear":[11],"on":[12,17],"occasion.":[13],"The":[14,33],"authors\u2019":[15],"study":[16],"a":[21],"class":[22],"exponential":[24],"logarithmic":[26],"functions":[27],"is":[28],"presented":[29],"in":[30,54],"this":[31,55],"publication.":[32],"paper":[34],"includes":[35],"several":[36],"examples":[37],"that":[38],"demonstrate":[39],"evaluation":[41],"analytical":[44],"parts":[45],"multi-dimensional":[48],"integral":[49],"derived.":[50],"All":[51],"results":[53],"work":[56],"are":[57],"new.":[58]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2022-02-08T00:00:00"}
