A new approach to generalized Fibonacci and Lucas numbers with binomial coefficients

Gulec, Hasan Huseyin; Taşkara, Necati; Uslu, Kemal

doi:10.1016/j.amc.2013.05.043

Cited by 19 publications

(16 citation statements)

References 9 publications

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“…Yet, studying Fibonacci polynomials for their own sake provides us with a clearer idea concerning their combinatorial and analytic properties. A great deal of mathematical ingenuity has been invested in developing identities involving Fibonacci polynomials, Fibonacci numbers, and their generalizations, see [11][12][13][19][20][21] In order to study Fibonacci polynomials, one may consider linking Fibonacci polynomials to other well-studied polynomials, such as Chebyshev polynomials. Chebyshev polynomials of the first and second kinds, T n (x) and U n (x) respectively, are subfamilies of the larger class of Jacobi polynomials.…”

Section: Introductionmentioning

confidence: 99%

New hypergeometric connection formulae between Fibonacci and Chebyshev polynomials

et al. 2015

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Abstract. We establish new connection formulae between Fibonacci polynomials and Chebyshev polynomials of the first and second kinds. These formulae are expressed in terms of certain values of hypergeometric functions of the type 2 F 1 . Consequently, we obtain some new expressions for the celebrated Fibonacci numbers and their derivatives sequences. Moreover, we evaluate some definite integrals involving products of Fibonacci and Chebyshev polynomials.

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Section: Introductionmentioning

confidence: 99%

New hypergeometric connection formulae between Fibonacci and Chebyshev polynomials

et al. 2015

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“…For more details on the Fibonacci sequence and its relation with the Golden Ratio see for instance [4,6,7,10].…”

Section: Introductionmentioning

confidence: 99%

Generalized Golden Ratios defined by means

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et al. 2015

Applied Mathematics and Computation

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“…Falcon and Plaza [4] introduced general -Fibonacci numbers and gave some properties of these numbers. Guleç et al [5] presented some properties of generalized Fibonacci numbers with binomial coefficients.…”

Section: Introductionmentioning

confidence: 99%