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dc.contributor.authorSharma, Sunil Kumar
dc.contributor.authorKhan, Waseem Ahmad
dc.contributor.authorRyoo, Cheon-Seoung
dc.contributor.authorDuran, Uğur
dc.date.accessioned2022-11-21T06:47:45Z
dc.date.available2022-11-21T06:47:45Z
dc.date.issued2022en_US
dc.identifier.citationSharma, S.K., Khan, W.A., Ryoo, C.-S., Duran, U. (2022). Diverse Properties and Approximate Roots for a Novel Kinds of the (p,q)-Cosine and (p,q)-Sine Geometric Polynomials. Mathematics, 10 (15), art. no. 2709. https://doi.org/10.3390/math10152709en_US
dc.identifier.urihttps://doi.org/10.3390/math10152709
dc.identifier.urihttps://hdl.handle.net/20.500.12508/2289
dc.description.abstractUtilizing (p, q)-numbers and (p, q)-concepts, in 2016, Duran et al. considered (p, q)-Genocchi numbers and polynomials, (p, q)-Bernoulli numbers and polynomials and (p, q)-Euler polynomials and numbers and provided multifarious formulas and properties for these polynomials. Inspired and motivated by this consideration, many authors have introduced (p, q)-special polynomials and numbers and have described some of their properties and applications. In this paper, using the (p, q)-cosine polynomials and (p, q)-sine polynomials, we consider a novel kinds of (p, q)-extensions of geometric polynomials and acquire several properties and identities by making use of some series manipulation methods. Furthermore, we compute the (p, q)-integral representations and (p, q)-derivative operator rules for the new polynomials. Additionally, we determine the movements of the approximate zerosof the two mentioned polynomials in a complex plane, utilizing the Newton method, and we illustrate them using figures.en_US
dc.language.isoengen_US
dc.publisherMDPIen_US
dc.relation.isversionof10.3390/math10152709en_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subject(p, q)-calculusen_US
dc.subjectCosine polynomialsen_US
dc.subject(p, q)-geometric polynomialsen_US
dc.subject(p, q)-trigonometric functionsen_US
dc.subjectGeometric polynomialsen_US
dc.subjectSine polynomialsen_US
dc.subject.classificationEuler Polynomials
dc.subject.classificationBernoulli Numbers
dc.subject.classificationDegenerate
dc.subject.classificationMathematics
dc.subject.classificationMathematics - Functional Analysis - Statistical Convergence
dc.subject.otherNumbers
dc.titleDiverse Properties and Approximate Roots for a Novel Kinds of the (p, q)-Cosine and (p, q)-Sine Geometric Polynomialsen_US
dc.typearticleen_US
dc.relation.journalMathematicsen_US
dc.contributor.departmentMühendislik ve Doğa Bilimleri Fakültesi -- Mühendislik Temel Bilimleri Bölümüen_US
dc.identifier.volume10en_US
dc.identifier.issue15en_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.contributor.isteauthorDuran, Uğur
dc.relation.indexWeb of Science - Scopusen_US
dc.relation.indexWeb of Science Core Collection - Science Citation Index Expanded


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