Results 21 to 30 of about 524,049 (276)
Generalized Fibonacci polynomials and Fibonomial coefficients [PDF]
Annals of Combinatorics, 2013 The focus of this paper is the study of generalized Fibonacci polynomials and Fibonomial coefficients. The former are polynomials {n} in variables s and t given by {0} = 0, {1} = 1, and {n} = s{n-1}+t{n-2} for n ge 2. The latter are defined by {n choose k} = {n}!/({k}!{n-k}!) where {n}! = {1}{2}...{n}.
Tewodros Amdeberhan +3 more
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Sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials. [PDF]
J Inequal Appl, 2018 In this paper, we consider sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials and derive Fourier series expansions of functions associated with them. From these Fourier series expansions, we can express those
Kim T, Kim DS, Dolgy DV, Park JW.
europepmc +2 more sources
On Convolved Generalized Fibonacci and Lucas Polynomials [PDF]
Applied Mathematics and Computation, 2013 We define the convolved h(x)-Fibonacci polynomials as an extension of the classical convolved Fibonacci numbers. Then we give some combinatorial formulas involving the h(x)-Fibonacci and h(x)-Lucas polynomials.
Ramírez, José L.
core +4 more sources
arXiv, 2009 We show that the Conway polynomials of Fibonacci links are Fibonacci polynomials modulo 2. We deduce that, when $ n \not\equiv 0 \Mod 4$ and $(n,j) \neq (3,3),$ the Fibonacci knot $ \cF_j^{(n)} $ is not a Lissajous knot.Comment: 7p ...
Koseleff, Pierre-Vincent, Pecker, Daniel
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Indian Journal of Pure and Applied Mathematics, 2023 In this paper, by the help the F-vacuum operator, we define the harmonic Fibonacci polynomials and harmonic based F-exponential generating function. The harmonic based F-exponential generating function is obtained for the Bernoulli-F polynomials, the Euler-Fibonacci numbers, the Euler-Fibonacci polynomials and the Bernoulli-Fibonacci numbers, and their
TUĞLU, NAİM +2 more
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Fibonacci Polynomials and Determinant Identities [PDF]
Turkish Journal of Analysis and Number Theory, 2014 The Fibonacci polynomials and Lucas polynomials are famous for possessing wonderful and amazing properties and identities. In this paper, some determinant identities of Fibonacci polynomials are describe. Entries of determinants are satisfying the recurrence relations of Fibonacci polynomials and Lucas polynomials.
Omprakash Sikhwal, Yashwant Vyas
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A New Class of q-Fibonacci Polynomials [PDF]
The Electronic Journal of Combinatorics, 2003 We introduce a new $q$-analogue of the Fibonacci polynomials and derive some of its properties. Extra attention is paid to a special case which has some interesting connections with Euler's pentagonal number theorem.
Johann Cigler
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Identities for the generalized Fibonacci polynomial [PDF]
INTEGERS 18B (2018).
http://math.colgate.edu/~integers/s18b2/s18b2.pdf, 2017 A second order polynomial sequence is of Fibonacci type (Lucas type) if its Binet formula is similar in structure to the Binet formula for the Fibonacci (Lucas) numbers. In this paper we generalize identities from Fibonacci numbers and Lucas numbers to Fibonacci type and Lucas type polynomials.
Flórez, R., McAnally, N., Mukherjee, A.
arxiv +4 more sources
Contemporary Mathematics, 2022 In this research article, we build and implement an efficient spectral algorithm for handling linear/nonlinear mixed Volterra-Fredholm integro-differential equations.
Emad M. Abo-Eldahab +2 more
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(2, k)-Distance Fibonacci Polynomials [PDF]
Symmetry, 2021 In this paper we introduce and study (2,k)-distance Fibonacci polynomials which are natural extensions of (2,k)-Fibonacci numbers. We give some properties of these polynomials—among others, a graph interpretation and matrix generators. Moreover, we present some connections of (2,k)-distance Fibonacci polynomials with Pascal’s triangle.
Dorota Bród, Andrzej Włoch
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