{"id":"https://openalex.org/W2033574984","doi":"https://doi.org/10.1155/2013/242815","title":"A Determinant Expression for the Generalized Bessel Polynomials","display_name":"A Determinant Expression for the Generalized Bessel Polynomials","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2033574984","doi":"https://doi.org/10.1155/2013/242815","mag":"2033574984"},"language":"en","primary_location":{"id":"doi:10.1155/2013/242815","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/242815","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/242815.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2013/242815.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068812894","display_name":"Sheng-Liang Yang","orcid":"https://orcid.org/0000-0002-9314-346X"},"institutions":[{"id":"https://openalex.org/I22716506","display_name":"Lanzhou University of Technology","ror":"https://ror.org/03panb555","country_code":"CN","type":"education","lineage":["https://openalex.org/I22716506"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Sheng-liang Yang","raw_affiliation_strings":["Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China","institution_ids":["https://openalex.org/I22716506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102823709","display_name":"Sai-Nan Zheng","orcid":"https://orcid.org/0000-0003-4932-8464"},"institutions":[{"id":"https://openalex.org/I22716506","display_name":"Lanzhou University of Technology","ror":"https://ror.org/03panb555","country_code":"CN","type":"education","lineage":["https://openalex.org/I22716506"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Sai-nan Zheng","raw_affiliation_strings":["Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China","institution_ids":["https://openalex.org/I22716506"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5068812894"],"corresponding_institution_ids":["https://openalex.org/I22716506"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.5636,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.62841678,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.9886000156402588,"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/T11567","display_name":"semigroups and automata theory","score":0.9424999952316284,"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/bessel-function","display_name":"Bessel function","score":0.9174689054489136},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8538154363632202},{"id":"https://openalex.org/keywords/bessel-polynomials","display_name":"Bessel polynomials","score":0.7512309551239014},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5978337526321411},{"id":"https://openalex.org/keywords/catalan-number","display_name":"Catalan number","score":0.5950920581817627},{"id":"https://openalex.org/keywords/expression","display_name":"Expression (computer science)","score":0.582817554473877},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5734407305717468},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5418203473091125},{"id":"https://openalex.org/keywords/bessel-process","display_name":"Bessel process","score":0.5318063497543335},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.43727946281433105},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3757876753807068},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.3649112582206726},{"id":"https://openalex.org/keywords/wilson-polynomials","display_name":"Wilson polynomials","score":0.24247145652770996},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23228022456169128},{"id":"https://openalex.org/keywords/difference-polynomials","display_name":"Difference polynomials","score":0.22137105464935303},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.20517703890800476},{"id":"https://openalex.org/keywords/gegenbauer-polynomials","display_name":"Gegenbauer polynomials","score":0.10294461250305176},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.04313918948173523}],"concepts":[{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.9174689054489136},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8538154363632202},{"id":"https://openalex.org/C73295869","wikidata":"https://www.wikidata.org/wiki/Q4896402","display_name":"Bessel polynomials","level":5,"score":0.7512309551239014},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5978337526321411},{"id":"https://openalex.org/C43929256","wikidata":"https://www.wikidata.org/wiki/Q270513","display_name":"Catalan number","level":2,"score":0.5950920581817627},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.582817554473877},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5734407305717468},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5418203473091125},{"id":"https://openalex.org/C118532472","wikidata":"https://www.wikidata.org/wiki/Q4896405","display_name":"Bessel process","level":5,"score":0.5318063497543335},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43727946281433105},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3757876753807068},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.3649112582206726},{"id":"https://openalex.org/C43176163","wikidata":"https://www.wikidata.org/wiki/Q8023263","display_name":"Wilson polynomials","level":4,"score":0.24247145652770996},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23228022456169128},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.22137105464935303},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.20517703890800476},{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.10294461250305176},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.04313918948173523},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2013/242815","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/242815","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/242815.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1394808110","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1394808110","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:242815","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2013/242815.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:59f1eadacfab45eeb1874c0737b094e5","is_oa":true,"landing_page_url":"https://doaj.org/article/59f1eadacfab45eeb1874c0737b094e5","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":"Journal of Applied Mathematics, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/242815","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/242815","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/242815.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1708441129","display_name":null,"funder_award_id":"11261032","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5317292085","display_name":null,"funder_award_id":"1010RJZA049","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6403820174","display_name":null,"funder_award_id":"1010RJZA049","funder_id":"https://openalex.org/F4320322880","funder_display_name":"Natural Science Foundation of Gansu Province"},{"id":"https://openalex.org/G912056000","display_name":null,"funder_award_id":"11261032","funder_id":"https://openalex.org/F4320322880","funder_display_name":"Natural Science Foundation of Gansu Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322880","display_name":"Natural Science Foundation of Gansu Province","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2033574984.pdf","grobid_xml":"https://content.openalex.org/works/W2033574984.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W884356426","https://openalex.org/W1994416105","https://openalex.org/W1994702412","https://openalex.org/W2009605145","https://openalex.org/W2028017249","https://openalex.org/W2034597036","https://openalex.org/W2037796089","https://openalex.org/W2038671824","https://openalex.org/W2048936241","https://openalex.org/W2079677302","https://openalex.org/W2087830437","https://openalex.org/W2130012544","https://openalex.org/W2135276434","https://openalex.org/W2918299014","https://openalex.org/W3042508952"],"related_works":["https://openalex.org/W4236729297","https://openalex.org/W2011121568","https://openalex.org/W2073673068","https://openalex.org/W884356426","https://openalex.org/W3023547025","https://openalex.org/W2034875467","https://openalex.org/W2273780518","https://openalex.org/W4361230481","https://openalex.org/W2506296488","https://openalex.org/W2131500575"],"abstract_inverted_index":{"Using":[0],"the":[1,11,27,34,41],"exponential":[2],"Riordan":[3],"arrays,":[4],"we":[5,21],"show":[6],"that":[7],"a":[8,23,32],"variation":[9],"of":[10,17,43],"generalized":[12,28],"Bessel":[13,29,35],"polynomial":[14,36],"sequence":[15],"is":[16,37],"Sheffer":[18],"type,":[19],"and":[20],"obtain":[22],"determinant":[24,40],"formula":[25],"for":[26],"polynomials.":[30],"As":[31],"result,":[33],"represented":[38],"as":[39],"entries":[42],"which":[44],"involve":[45],"Catalan":[46],"numbers.":[47]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
