{"id":"https://openalex.org/W2045154321","doi":"https://doi.org/10.1016/s0196-8858(02)00017-9","title":"An integral formula for generalized Gegenbauer polynomials and Jacobi polynomials","display_name":"An integral formula for generalized Gegenbauer polynomials and Jacobi polynomials","publication_year":2002,"publication_date":"2002-08-01","ids":{"openalex":"https://openalex.org/W2045154321","doi":"https://doi.org/10.1016/s0196-8858(02)00017-9","mag":"2045154321"},"language":"en","primary_location":{"id":"doi:10.1016/s0196-8858(02)00017-9","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0196-8858(02)00017-9","pdf_url":null,"source":{"id":"https://openalex.org/S164906323","display_name":"Advances in Applied Mathematics","issn_l":"0196-8858","issn":["0196-8858","1090-2074"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101667089","display_name":"Yuan Xu","orcid":"https://orcid.org/0000-0001-9228-3818"},"institutions":[{"id":"https://openalex.org/I181233156","display_name":"University of Oregon","ror":"https://ror.org/0293rh119","country_code":"US","type":"education","lineage":["https://openalex.org/I181233156"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yuan Xu","raw_affiliation_strings":["Department of Mathematics, University of Oregon, Eugene, OR 97403-1222, USA","Department of Mathematics, University of Oregon, Eugene, OR 97403\u20101222, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Oregon, Eugene, OR 97403-1222, USA","institution_ids":["https://openalex.org/I181233156"]},{"raw_affiliation_string":"Department of Mathematics, University of Oregon, Eugene, OR 97403\u20101222, USA","institution_ids":["https://openalex.org/I181233156"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101667089"],"corresponding_institution_ids":["https://openalex.org/I181233156"],"apc_list":{"value":2670,"currency":"USD","value_usd":2670},"apc_paid":null,"fwci":1.0958,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.74713896,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"29","issue":"2","first_page":"328","last_page":"343"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9997000098228455,"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":0.9997000098228455,"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9761000275611877,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.873858630657196},{"id":"https://openalex.org/keywords/gegenbauer-polynomials","display_name":"Gegenbauer polynomials","score":0.8650919198989868},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.8444558382034302},{"id":"https://openalex.org/keywords/jacobi-polynomials","display_name":"Jacobi polynomials","score":0.8320716023445129},{"id":"https://openalex.org/keywords/discrete-orthogonal-polynomials","display_name":"Discrete orthogonal polynomials","score":0.8078407049179077},{"id":"https://openalex.org/keywords/wilson-polynomials","display_name":"Wilson polynomials","score":0.7918686866760254},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.7778327465057373},{"id":"https://openalex.org/keywords/difference-polynomials","display_name":"Difference polynomials","score":0.7015543580055237},{"id":"https://openalex.org/keywords/mehler\u2013heine-formula","display_name":"Mehler\u2013Heine formula","score":0.6326253414154053},{"id":"https://openalex.org/keywords/hahn-polynomials","display_name":"Hahn polynomials","score":0.6076465845108032},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4260820746421814}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.873858630657196},{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.8650919198989868},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.8444558382034302},{"id":"https://openalex.org/C48490523","wikidata":"https://www.wikidata.org/wiki/Q371631","display_name":"Jacobi polynomials","level":3,"score":0.8320716023445129},{"id":"https://openalex.org/C52537462","wikidata":"https://www.wikidata.org/wiki/Q5282055","display_name":"Discrete orthogonal polynomials","level":3,"score":0.8078407049179077},{"id":"https://openalex.org/C43176163","wikidata":"https://www.wikidata.org/wiki/Q8023263","display_name":"Wilson polynomials","level":4,"score":0.7918686866760254},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.7778327465057373},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.7015543580055237},{"id":"https://openalex.org/C118431652","wikidata":"https://www.wikidata.org/wiki/Q17098827","display_name":"Mehler\u2013Heine formula","level":5,"score":0.6326253414154053},{"id":"https://openalex.org/C61349858","wikidata":"https://www.wikidata.org/wiki/Q1568814","display_name":"Hahn polynomials","level":5,"score":0.6076465845108032},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4260820746421814}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/s0196-8858(02)00017-9","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0196-8858(02)00017-9","pdf_url":null,"source":{"id":"https://openalex.org/S164906323","display_name":"Advances in Applied Mathematics","issn_l":"0196-8858","issn":["0196-8858","1090-2074"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.8.2090","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.8.2090","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://darkwing.uoregon.edu/~yuan/paper/Jacobi.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1506933769","https://openalex.org/W1999014216","https://openalex.org/W2028420334","https://openalex.org/W2070503385","https://openalex.org/W2319345516","https://openalex.org/W4230199773"],"related_works":["https://openalex.org/W2045154321","https://openalex.org/W34992575","https://openalex.org/W3147630167","https://openalex.org/W2158826266","https://openalex.org/W3161996133","https://openalex.org/W2504939013","https://openalex.org/W3209953184","https://openalex.org/W1651872008","https://openalex.org/W4287597771","https://openalex.org/W2099676275"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
