{"id":"https://openalex.org/W7147547579","doi":"https://doi.org/10.25430/pupj-drna-2026-1-9","title":"q\u2212extensions for the U\u2212Bernoulli and U\u2212Euler polynomials","display_name":"q\u2212extensions for the U\u2212Bernoulli and U\u2212Euler polynomials","publication_year":2026,"publication_date":"2026-03-31","ids":{"openalex":"https://openalex.org/W7147547579","doi":"https://doi.org/10.25430/pupj-drna-2026-1-9"},"language":"en","primary_location":{"id":"doi:10.25430/pupj-drna-2026-1-9","doi":"https://doi.org/10.25430/pupj-drna-2026-1-9","is_oa":true,"landing_page_url":"https://doi.org/10.25430/pupj-drna-2026-1-9","pdf_url":null,"source":{"id":"https://openalex.org/S2739139558","display_name":"Dolomites Research Notes on Approximation","issn_l":"2035-6803","issn":["2035-6803"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310317600","host_organization_name":"Padova University Press","host_organization_lineage":["https://openalex.org/P4310317600"],"host_organization_lineage_names":["Padova University Press"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.25430/pupj-drna-2026-1-9","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034386749","display_name":"Semra Ku\u015f","orcid":"https://orcid.org/0000-0001-8694-8254","observed_orcids":["https://orcid.org/0000-0001-8694-8254"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Semra Ku\u015f","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075278042","display_name":"William Ram\u00edrez","orcid":"https://orcid.org/0000-0003-4675-0221","observed_orcids":["https://orcid.org/0000-0003-4675-0221"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"William Ram\u00edrez","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077546142","display_name":"Letelier Castilla","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Letelier Castilla","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5057247491","display_name":"Mohammed Fadel","orcid":"https://orcid.org/0000-0002-6206-9113","observed_orcids":["https://orcid.org/0000-0002-6206-9113"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mohammed Fadel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.7573000192642212,"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":0.7573000192642212,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.18690000474452972,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.02459999918937683,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/q-bernoulli-polynomials","display_name":"q-Bernoulli polynomials","score":0.8870000243186951},{"id":"https://openalex.org/keywords/q-euler-polynomials","display_name":"q-Euler polynomials","score":0.8560000061988831},{"id":"https://openalex.org/keywords/rogers-szego-polynomials","display_name":"Rogers-Szeg\u0151 polynomials","score":0.9020000100135803},{"id":"https://openalex.org/keywords/q-bernoulli-numbers","display_name":"q-Bernoulli numbers","score":0.9599999785423279},{"id":"https://openalex.org/keywords/generating-functions","display_name":"generating functions","score":0.7820000052452087},{"id":"https://openalex.org/keywords/summation-formulas","display_name":"summation formulas","score":0.953000009059906},{"id":"https://openalex.org/keywords/connection-formulas","display_name":"connection formulas","score":0.9549999833106995}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7070000171661377},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.588100016117096},{"id":"https://openalex.org/C52537462","wikidata":"https://www.wikidata.org/wiki/Q5282055","display_name":"Discrete orthogonal polynomials","level":3,"score":0.5813000202178955},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.5740000009536743},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.5637000203132629},{"id":"https://openalex.org/C43176163","wikidata":"https://www.wikidata.org/wiki/Q8023263","display_name":"Wilson polynomials","level":4,"score":0.4779999852180481},{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.4756999909877777},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.43939998745918274},{"id":"https://openalex.org/C61349858","wikidata":"https://www.wikidata.org/wiki/Q1568814","display_name":"Hahn polynomials","level":5,"score":0.4268999993801117},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4180000126361847},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3898000121116638},{"id":"https://openalex.org/C171686973","wikidata":"https://www.wikidata.org/wiki/Q17098676","display_name":"Macdonald polynomials","level":4,"score":0.3874000012874603},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.328000009059906},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32249999046325684},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.31369999051094055},{"id":"https://openalex.org/C48490523","wikidata":"https://www.wikidata.org/wiki/Q371631","display_name":"Jacobi polynomials","level":3,"score":0.30469998717308044},{"id":"https://openalex.org/C146922319","wikidata":"https://www.wikidata.org/wiki/Q4298935","display_name":"Schur polynomial","level":5,"score":0.2671999931335449}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.25430/pupj-drna-2026-1-9","doi":"https://doi.org/10.25430/pupj-drna-2026-1-9","is_oa":true,"landing_page_url":"https://doi.org/10.25430/pupj-drna-2026-1-9","pdf_url":null,"source":{"id":"https://openalex.org/S2739139558","display_name":"Dolomites Research Notes on Approximation","issn_l":"2035-6803","issn":["2035-6803"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310317600","host_organization_name":"Padova University Press","host_organization_lineage":["https://openalex.org/P4310317600"],"host_organization_lineage_names":["Padova University Press"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.25430/pupj-drna-2026-1-9","doi":"https://doi.org/10.25430/pupj-drna-2026-1-9","is_oa":true,"landing_page_url":"https://doi.org/10.25430/pupj-drna-2026-1-9","pdf_url":null,"source":{"id":"https://openalex.org/S2739139558","display_name":"Dolomites Research Notes on Approximation","issn_l":"2035-6803","issn":["2035-6803"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310317600","host_organization_name":"Padova University Press","host_organization_lineage":["https://openalex.org/P4310317600"],"host_organization_lineage_names":["Padova University Press"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1567373341","https://openalex.org/W2068905081","https://openalex.org/W2073803111","https://openalex.org/W2481303708","https://openalex.org/W2146331499","https://openalex.org/W1999363819","https://openalex.org/W2066491650","https://openalex.org/W1981741991","https://openalex.org/W2323445810","https://openalex.org/W2113221414"],"abstract_inverted_index":{"This":[0],"paper":[1],"defines":[2],"the":[3,19,32,49],"q\u2212U\u2212Bernoulli,":[4],"q\u2212U\u2212Euler":[5],"polynomials":[6,21,27,54],"and":[7,9,31,52,60],"numbers":[8,34],"obtains":[10],"some":[11,40],"of":[12],"their":[13],"feature":[14],"relations.":[15,62],"We":[16],"also":[17],"explore":[18],"q\u2212U\u2212Bernoulli":[20],"Ms":[22],"(\u03b3,":[23,29],"q)":[24,30],",":[25],"Rogers-Szeg\u00f6":[26],"Hs":[28],"q\u2212Bernoulli":[33],"Bs":[35],"(q)":[36],"are":[37],"related":[38],"via":[39],"connection":[41],"formulas.":[42],"Further,":[43],"we":[44],"define":[45],"various":[46],"properties":[47],"for":[48],"q\u2212extensions":[50],"U\u2212Bernoulli":[51],"U\u2212Euler":[53],"like":[55],"generating":[56],"functions,":[57],"q\u2212partial":[58],"derivatives":[59],"summation":[61]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-04-02T00:00:00"}
