{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-JSUIUD70/2860ab75-f63c-42cb-857e-eb67036f1ad6/PDF","dcterms:extent":"249 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-JSUIUD70/0b05fe76-1c50-4121-bbf4-efb7df6c8621/TEXT","dcterms:extent":"23 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2025","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2025"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-JSUIUD70","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2020","dc:creator":"Komatsu, Takao","dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:18"},{"@xml:lang":"sl","#text":"str. 163-177"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:39896579","URN:URN:NBN:SI:doc-JSUIUD70"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"en","#text":"Bernoulli numbers"},{"@xml:lang":"sl","#text":"Bernoullijeva števila"},{"@xml:lang":"en","#text":"degenerate Bernoulli numbers"},{"@xml:lang":"sl","#text":"degenerirana Bernoullijeva števila"},{"@xml:lang":"sl","#text":"determinante"},{"@xml:lang":"en","#text":"determinants"},{"@xml:lang":"sl","#text":"hipergeometrijska Bernoullijeva števila"},{"@xml:lang":"sl","#text":"hipergeometrijska Cauchyjeva števila"},{"@xml:lang":"sl","#text":"hipergeometrijske funkcije"},{"@xml:lang":"en","#text":"hypergeometric Bernoulli numbers"},{"@xml:lang":"en","#text":"hypergeometric Cauchy numbers"},{"@xml:lang":"en","#text":"hypergeometric functions"},{"@xml:lang":"en","#text":"recurrence relations"},{"@xml:lang":"sl","#text":"rekurzivne zveze"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Hypergeometric degenerate Bernoulli polynomials and numbers|"},"dc:description":[{"@xml:lang":"sl","#text":"Carlitz defined the degenerate Bernoulli polynomials ?$\\beta_n(\\lambda,x)$? by means of the generating function ?$t\\left((1+\\lambda t)^{1/\\lambda}-1\\right)^{-1} (1+\\lambda t)^{x/\\lambda})$?. In 1875, Glaisher gave several interesting determinant expressions of numbers, including Bernoulli, Cauchy and Euler numbers. In this paper, we show some expressions and properties of hypergeometric degenerate Bernoulli polynomials ?$\\beta_{N,n}(\\lambda, x)$? and numbers, in particular, in terms of determinants. The coefficients of the polynomial ?$\\beta_n(\\lambda, 0)$? were completely determined by Howard in 1996. We determine the coefficients of the polynomial ?$\\beta_{N,n}(\\lambda, 0)$?. Hypergeometric Bernoulli numbers and hypergeometric Cauchy numbers appear in the coefficients"},{"@xml:lang":"sl","#text":"Carlitz je definiral degenerirane Bernoullijeve polinome ?$\\beta_n(\\lambda, x)$? s pomočjo rodovne funkcije ?$t\\left((1+\\lambda t)^{1/\\lambda}-1\\right)^{-1} (1+\\lambda t)^{x/\\lambda})$?. Leta 1875 je Glaisher predstavil zanimive determinantne izraze različnih števil, vključno z Bernoullijevimi, Cauchyjevimi in Eulerjevimi števili. V članku dokažemo nekaj izrazov in lastnosti hipergeometrijskih degeneriranih Bernoullijevih polinomov ?$\\beta_{N,n}(\\lambda,x)$? in števil, še posebej takih, ki se izražajo s pomočjo determinant. Koeficiente polinoma ?$\\beta_n(\\lambda, 0)$? je v celoti določil Howard leta 1996. Določimo koeficiente polinoma ?$\\beta_{N,n}(\\lambda, 0)$?. V teh koeficientih nastopajo hipergeometrijska Bernoullijeva števila in hipergeometrijska Cauchyjeva števila"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:doc-JSUIUD70","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-JSUIUD70"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-JSUIUD70/2860ab75-f63c-42cb-857e-eb67036f1ad6/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by/4.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-JSUIUD70/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-JSUIUD70"}}}}