{"id":"https://openalex.org/W2889588140","doi":"https://doi.org/10.3390/sym10100451","title":"On p-adic Integral Representation of q-Bernoulli Numbers Arising from Two Variable q-Bernstein Polynomials","display_name":"On p-adic Integral Representation of q-Bernoulli Numbers Arising from Two Variable q-Bernstein Polynomials","publication_year":2018,"publication_date":"2018-10-01","ids":{"openalex":"https://openalex.org/W2889588140","doi":"https://doi.org/10.3390/sym10100451","mag":"2889588140"},"language":"en","primary_location":{"id":"doi:10.3390/sym10100451","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10100451","pdf_url":"https://www.mdpi.com/2073-8994/10/10/451/pdf?version=1538388138","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/2073-8994/10/10/451/pdf?version=1538388138","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003571699","display_name":"Dae San Kim","orcid":"https://orcid.org/0000-0001-9599-7015"},"institutions":[{"id":"https://openalex.org/I148751991","display_name":"Sogang University","ror":"https://ror.org/056tn4839","country_code":"KR","type":"education","lineage":["https://openalex.org/I148751991"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Dae Kim","raw_affiliation_strings":["Department of Mathematics, Sogang University, Seoul 121-742, Korea"],"raw_orcid":"https://orcid.org/0000-0001-9599-7015","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sogang University, Seoul 121-742, Korea","institution_ids":["https://openalex.org/I148751991"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100653780","display_name":"Taekyun Kim","orcid":"https://orcid.org/0000-0002-3731-7023"},"institutions":[{"id":"https://openalex.org/I161024014","display_name":"Kwangwoon University","ror":"https://ror.org/02e9zc863","country_code":"KR","type":"education","lineage":["https://openalex.org/I161024014"]},{"id":"https://openalex.org/I198091727","display_name":"Tiangong University","ror":"https://ror.org/00xsr9m91","country_code":"CN","type":"education","lineage":["https://openalex.org/I198091727"]}],"countries":["CN","KR"],"is_corresponding":false,"raw_author_name":"Taekyun Kim","raw_affiliation_strings":["Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea","Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea","institution_ids":["https://openalex.org/I161024014"]},{"raw_affiliation_string":"Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China","institution_ids":["https://openalex.org/I198091727"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111969523","display_name":"C. S. Ryoo","orcid":null},"institutions":[{"id":"https://openalex.org/I112728665","display_name":"Hannam University","ror":"https://ror.org/01cwbae71","country_code":"KR","type":"education","lineage":["https://openalex.org/I112728665"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Cheon Ryoo","raw_affiliation_strings":["Department of Mathematics, Hannam University, Daejeon 306-791, Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hannam University, Daejeon 306-791, Korea","institution_ids":["https://openalex.org/I112728665"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086876412","display_name":"Yonghong Yao","orcid":"https://orcid.org/0000-0002-0452-785X"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]},{"id":"https://openalex.org/I198091727","display_name":"Tiangong University","ror":"https://ror.org/00xsr9m91","country_code":"CN","type":"education","lineage":["https://openalex.org/I198091727"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yonghong Yao","raw_affiliation_strings":["Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China","Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China"],"raw_orcid":"https://orcid.org/0000-0002-0452-785X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China","institution_ids":["https://openalex.org/I198091727"]},{"raw_affiliation_string":"Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China","institution_ids":["https://openalex.org/I150229711"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5111969523"],"corresponding_institution_ids":["https://openalex.org/I112728665"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.9753,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.73568095,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"10","issue":"10","first_page":"451","last_page":"451"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9997000098228455,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9889000058174133,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.98580002784729,"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/mathematics","display_name":"Mathematics","score":0.7563838958740234},{"id":"https://openalex.org/keywords/bernoulli-polynomials","display_name":"Bernoulli polynomials","score":0.6091445684432983},{"id":"https://openalex.org/keywords/bernstein-polynomial","display_name":"Bernstein polynomial","score":0.6077247858047485},{"id":"https://openalex.org/keywords/difference-polynomials","display_name":"Difference polynomials","score":0.5890085101127625},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5658308863639832},{"id":"https://openalex.org/keywords/hahn-polynomials","display_name":"Hahn polynomials","score":0.5439531803131104},{"id":"https://openalex.org/keywords/wilson-polynomials","display_name":"Wilson polynomials","score":0.5242559909820557},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.512248694896698},{"id":"https://openalex.org/keywords/macdonald-polynomials","display_name":"Macdonald polynomials","score":0.5100498795509338},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.4851594567298889},{"id":"https://openalex.org/keywords/discrete-orthogonal-polynomials","display_name":"Discrete orthogonal polynomials","score":0.47582629323005676},{"id":"https://openalex.org/keywords/bernoulli-number","display_name":"Bernoulli number","score":0.4650757312774658},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4489596486091614},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4161752760410309},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39935198426246643},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3943134844303131},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35800206661224365},{"id":"https://openalex.org/keywords/gegenbauer-polynomials","display_name":"Gegenbauer polynomials","score":0.24817940592765808},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18965014815330505}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7563838958740234},{"id":"https://openalex.org/C196172290","wikidata":"https://www.wikidata.org/wiki/Q2346201","display_name":"Bernoulli polynomials","level":4,"score":0.6091445684432983},{"id":"https://openalex.org/C34179328","wikidata":"https://www.wikidata.org/wiki/Q826841","display_name":"Bernstein polynomial","level":2,"score":0.6077247858047485},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.5890085101127625},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5658308863639832},{"id":"https://openalex.org/C61349858","wikidata":"https://www.wikidata.org/wiki/Q1568814","display_name":"Hahn polynomials","level":5,"score":0.5439531803131104},{"id":"https://openalex.org/C43176163","wikidata":"https://www.wikidata.org/wiki/Q8023263","display_name":"Wilson polynomials","level":4,"score":0.5242559909820557},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.512248694896698},{"id":"https://openalex.org/C171686973","wikidata":"https://www.wikidata.org/wiki/Q17098676","display_name":"Macdonald polynomials","level":4,"score":0.5100498795509338},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.4851594567298889},{"id":"https://openalex.org/C52537462","wikidata":"https://www.wikidata.org/wiki/Q5282055","display_name":"Discrete orthogonal polynomials","level":3,"score":0.47582629323005676},{"id":"https://openalex.org/C129960964","wikidata":"https://www.wikidata.org/wiki/Q694114","display_name":"Bernoulli number","level":2,"score":0.4650757312774658},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4489596486091614},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4161752760410309},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39935198426246643},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3943134844303131},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35800206661224365},{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.24817940592765808},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18965014815330505},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym10100451","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10100451","pdf_url":"https://www.mdpi.com/2073-8994/10/10/451/pdf?version=1538388138","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:83b3addb80a84b01969277cd6286f682","is_oa":true,"landing_page_url":"https://doaj.org/article/83b3addb80a84b01969277cd6286f682","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 10, Iss 10, p 451 (2018)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym10100451","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10100451","pdf_url":"https://www.mdpi.com/2073-8994/10/10/451/pdf?version=1538388138","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W73282625","https://openalex.org/W884044826","https://openalex.org/W2009632155","https://openalex.org/W2017628160","https://openalex.org/W2025176194","https://openalex.org/W2033226573","https://openalex.org/W2060489440","https://openalex.org/W2076024609","https://openalex.org/W2090042883","https://openalex.org/W2346670179","https://openalex.org/W2885455801","https://openalex.org/W2894000865","https://openalex.org/W2897891732","https://openalex.org/W3005929113","https://openalex.org/W3104497548","https://openalex.org/W3167979964","https://openalex.org/W3204561724","https://openalex.org/W4244836872","https://openalex.org/W6802371298","https://openalex.org/W6826862833"],"related_works":["https://openalex.org/W1655787750","https://openalex.org/W2358005339","https://openalex.org/W1975493754","https://openalex.org/W2397989412","https://openalex.org/W2042658470","https://openalex.org/W3130486304","https://openalex.org/W3111285862","https://openalex.org/W2964158901","https://openalex.org/W2071226509","https://openalex.org/W2966884257"],"abstract_inverted_index":{"The":[0],"q-Bernoulli":[1,74,81,103],"numbers":[2,75,104],"and":[3,34,36,43,63,76],"polynomials":[4,33,42,62],"can":[5,67],"be":[6,68],"given":[7],"by":[8],"Witt\u2019s":[9],"type":[10],"formulas":[11],"as":[12],"p-adic":[13],"invariant":[14],"integrals":[15,54],"on":[16,55],"Z":[17,56],"p":[18,57],".":[19],"We":[20],"investigate":[21],"some":[22,77,100],"properties":[23,39],"for":[24,40,51,102],"them.":[25],"In":[26],"addition,":[27],"we":[28,46],"consider":[29],"two":[30,59,95],"variable":[31,60,96],"q-Bernstein":[32,61,97],"operators":[35],"derive":[37],"several":[38],"these":[41],"operators.":[44],"Next,":[45],"study":[47],"the":[48,52,73,87],"evaluation":[49],"problem":[50,88],"double":[53],"of":[58,72,80,89,94],"show":[64],"that":[65],"they":[66],"expressed":[69],"in":[70],"terms":[71],"special":[78],"values":[79],"polynomials.":[82,98],"This":[83],"is":[84],"generalized":[85],"to":[86],"evaluating":[90],"any":[91],"finite":[92],"product":[93],"Furthermore,":[99],"identities":[101],"are":[105],"found.":[106]},"counts_by_year":[{"year":2019,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2018-09-27T00:00:00"}