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- W2039482973 abstract "AbstractIn this paper, based on the (p, q)-Fibonacci polynomials un(x) and (p, q)-Lucas polynomials vn(x), we introduce the convolved (p, q)-Fibonacci polynomials un(r)(x), which generalize the convolved Fibonacci numbers, the convolved Pell polynomials, and the Gegenbauer polynomials. We give the expressions, expansions, recurrence relations and differential recurrence relations of un(r)(x), and establish the relations between un(r)(x), un(x) and vn(x). Moreover, we also study the determinantal representations of un(r)(x) and vn(x), and present an algebraic interpretation of the polynomials un(r)(x).Keywords: (p, q)-Fibonacci polynomials(p, q)-Lucas polynomialsconvolved (p, q)-Fibonacci polynomialscombinatorial identitiesdeterminantsAMS Classifications:: 05A1505A1911B39 AcknowledgmentsThe authors would like to thank the anonymous referee for his (her) valuable comments and suggestions.Disclosure statementNo potential conflict of interest was reported by the authors.Additional informationFundingThe first author is supported by the Zhejiang Provincial Natural Science Foundation of China [grant LY13A010016], and the ‘521’ Talents Program of Zhejiang Sci-Tech University [grant 11430132521303]." @default.
- W2039482973 created "2016-06-24" @default.
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- W2039482973 date "2015-02-05" @default.
- W2039482973 modified "2023-10-16" @default.
- W2039482973 title "Some results on convolved (<i>p</i>,<i>q</i>)-Fibonacci polynomials" @default.
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- W2039482973 doi "https://doi.org/10.1080/10652469.2015.1007502" @default.
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