{"id":"https://openalex.org/W3210709983","doi":"https://doi.org/10.3390/sym13112013","title":"Certain Finite Integrals Related to the Products of Special Functions","display_name":"Certain Finite Integrals Related to the Products of Special Functions","publication_year":2021,"publication_date":"2021-10-23","ids":{"openalex":"https://openalex.org/W3210709983","doi":"https://doi.org/10.3390/sym13112013","mag":"3210709983"},"language":"en","primary_location":{"id":"doi:10.3390/sym13112013","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13112013","pdf_url":"https://www.mdpi.com/2073-8994/13/11/2013/pdf?version=1635917557","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/2073-8994/13/11/2013/pdf?version=1635917557","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000770804","display_name":"Dinesh Kumar","orcid":"https://orcid.org/0000-0001-5415-1777"},"institutions":[{"id":"https://openalex.org/I2801834944","display_name":"Swami Keshwanand Rajasthan Agricultural University","ror":"https://ror.org/00j6r8583","country_code":"IN","type":"education","lineage":["https://openalex.org/I2801834944"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Dinesh Kumar","raw_affiliation_strings":["Department of Applied Sciences, College of Agriculture, Sumerpur-Pali, Agriculture University Jodhpur, Jodhpur 342304, India"],"affiliations":[{"raw_affiliation_string":"Department of Applied Sciences, College of Agriculture, Sumerpur-Pali, Agriculture University Jodhpur, Jodhpur 342304, India","institution_ids":["https://openalex.org/I2801834944"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075461829","display_name":"Fr\u00e9d\u00e9ric Ayant","orcid":"https://orcid.org/0000-0003-0651-294X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fr\u00e9d\u00e9ric Ayant","raw_affiliation_strings":["Coll\u00e9ge Jean L\u2019herminier, All\u00e9e des Nymph\u00e9as, 83500 La Seyne-sur-Mer, France","Department of Var, 83140 Six-Fours-les-Plages, France"],"affiliations":[{"raw_affiliation_string":"Coll\u00e9ge Jean L\u2019herminier, All\u00e9e des Nymph\u00e9as, 83500 La Seyne-sur-Mer, France","institution_ids":[]},{"raw_affiliation_string":"Department of Var, 83140 Six-Fours-les-Plages, France","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081644547","display_name":"Suphawat Asawasamrit","orcid":null},"institutions":[{"id":"https://openalex.org/I82828225","display_name":"King Mongkut's University of Technology North Bangkok","ror":"https://ror.org/04fy6jb97","country_code":"TH","type":"education","lineage":["https://openalex.org/I82828225"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Suphawat Asawasamrit","raw_affiliation_strings":["Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand","Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand"],"affiliations":[{"raw_affiliation_string":"Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]},{"raw_affiliation_string":"Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051443783","display_name":"Jessada Tariboon","orcid":"https://orcid.org/0000-0001-8185-3539"},"institutions":[{"id":"https://openalex.org/I82828225","display_name":"King Mongkut's University of Technology North Bangkok","ror":"https://ror.org/04fy6jb97","country_code":"TH","type":"education","lineage":["https://openalex.org/I82828225"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Jessada Tariboon","raw_affiliation_strings":["Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand","Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand"],"affiliations":[{"raw_affiliation_string":"Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]},{"raw_affiliation_string":"Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5051443783"],"corresponding_institution_ids":["https://openalex.org/I82828225"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.9127,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.72500936,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"13","issue":"11","first_page":"2013","last_page":"2013"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9900000095367432,"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"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9900000095367432,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9857000112533569,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/aleph","display_name":"Aleph","score":0.799426257610321},{"id":"https://openalex.org/keywords/multivariable-calculus","display_name":"Multivariable calculus","score":0.6965248584747314},{"id":"https://openalex.org/keywords/special-functions","display_name":"Special functions","score":0.6554424166679382},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6232001781463623},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5968953371047974},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5738470554351807},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5083438754081726},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.48966673016548157},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.43444231152534485},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3395213186740875},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22447872161865234},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11531457304954529},{"id":"https://openalex.org/keywords/particle-physics","display_name":"Particle physics","score":0.07741290330886841},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06546777486801147},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.0577164888381958}],"concepts":[{"id":"https://openalex.org/C2781424814","wikidata":"https://www.wikidata.org/wiki/Q15033","display_name":"Aleph","level":2,"score":0.799426257610321},{"id":"https://openalex.org/C117312493","wikidata":"https://www.wikidata.org/wiki/Q2035437","display_name":"Multivariable calculus","level":2,"score":0.6965248584747314},{"id":"https://openalex.org/C50757856","wikidata":"https://www.wikidata.org/wiki/Q867707","display_name":"Special functions","level":2,"score":0.6554424166679382},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6232001781463623},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5968953371047974},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5738470554351807},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5083438754081726},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.48966673016548157},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43444231152534485},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3395213186740875},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22447872161865234},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11531457304954529},{"id":"https://openalex.org/C109214941","wikidata":"https://www.wikidata.org/wiki/Q18334","display_name":"Particle physics","level":1,"score":0.07741290330886841},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06546777486801147},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0577164888381958},{"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},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13112013","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13112013","pdf_url":"https://www.mdpi.com/2073-8994/13/11/2013/pdf?version=1635917557","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:ea6f99c2299f434cb19d57386a22dc33","is_oa":true,"landing_page_url":"https://doaj.org/article/ea6f99c2299f434cb19d57386a22dc33","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-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 2013 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/11/2013/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13112013","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/sym13112013","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13112013","pdf_url":"https://www.mdpi.com/2073-8994/13/11/2013/pdf?version=1635917557","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/G5286180236","display_name":null,"funder_award_id":"KMUTNB-GRAD-59-02","funder_id":"https://openalex.org/F4320324344","funder_display_name":"King Mongkut's University of Technology North Bangkok"}],"funders":[{"id":"https://openalex.org/F4320324344","display_name":"King Mongkut's University of Technology North Bangkok","ror":"https://ror.org/04fy6jb97"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3210709983.pdf","grobid_xml":"https://content.openalex.org/works/W3210709983.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W191636288","https://openalex.org/W1004919192","https://openalex.org/W1535353586","https://openalex.org/W1981322360","https://openalex.org/W2080836771","https://openalex.org/W2131822683","https://openalex.org/W2157893421","https://openalex.org/W2427207976","https://openalex.org/W2521173918","https://openalex.org/W2764225417","https://openalex.org/W7034080840"],"related_works":["https://openalex.org/W2884886989","https://openalex.org/W4252973390","https://openalex.org/W2760103578","https://openalex.org/W4237684070","https://openalex.org/W636289703","https://openalex.org/W2185999197","https://openalex.org/W2742660818","https://openalex.org/W3023951268","https://openalex.org/W2969494638","https://openalex.org/W2606245706"],"abstract_inverted_index":{"The":[0,26,61],"aim":[1],"of":[2,14,24,28,41],"this":[3,29],"paper":[4],"is":[5],"to":[6,65],"establish":[7],"a":[8,37],"theorem":[9,30],"associated":[10],"with":[11],"the":[12,15,17,21],"product":[13],"Aleph-function,":[16,19],"multivariable":[18],"and":[20,35,51,70],"general":[22],"class":[23],"polynomials.":[25],"results":[27,43,63],"are":[31],"unified":[32],"in":[33,68],"nature":[34],"provide":[36],"very":[38],"large":[39],"number":[40],"analogous":[42],"(new":[44],"or":[45,55],"known)":[46],"involving":[47],"simpler":[48],"special":[49,59],"functions":[50],"polynomials":[52],"(of":[53],"one":[54],"several":[56],"variables)":[57],"as":[58],"cases.":[60],"derived":[62],"lead":[64],"significant":[66],"applications":[67],"physics":[69],"engineering":[71],"sciences.":[72]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
