Fibonacci polynomials
The sums of the reciprocals of Fibonacci polynomials and Lucas polynomials
... the Fibonacci polynomials and Lucas polynomials, and infinite sums derived from the reciprocals of the square of the Fibonacci polynomials and Lucas ...the Fibonacci ...
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Sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials
... Chebyshev polynomials of the second kind and of Fibonacci polynomials and derive Fourier series expansions of functions asso- ciated with ...Bernoulli polynomials and obtain some identities by ...
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Several identities involving the Fibonacci polynomials and Lucas polynomials
... In this paper, the authors consider infinite sums derived from the reciprocals of the Fibonacci polynomials and Lucas polynomials. Then applying the floor function to the reciprocals of these sums, the ...
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Closed Expressions of the Fibonacci Polynomials in Terms of Tridiagonal Determinants
... In the paper, the authors find a new closed expression for the Fibonacci polynomials and, consequently, for the Fibonacci numbers, in terms of a tridiagonal determinant.. Main results.[r] ...
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Solving linear integral equations with Fibonacci polynomials
... using Fibonacci polynomials with hat basis functions, in order to obtain a variational problem and reduce this one to a linear system, where its solution is to find the Fibonacci coefficients of the ...
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EXPRESSING SUMS OF FINITE PRODUCTS OF CHEBYSHEV POLYNOMIALS OF THE SECOND KIND AND OF FIBONACCI POLYNOMIALS BY SEVERAL ORTHOGONAL POLYNOMIALS
... associated with Jacobi polynomials, Discrete Dyn. Nat. Soc. 2012, Art. ID 584643, 11 pp. 12. T. Kim, D. S. Kim, D. V. Dolgy, J.-W. Park Sums of finite products of Chebyshev polyno- mials of the second kind and of ...
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Some new results for the (p,q) Fibonacci and Lucas polynomials
... Lucas polynomials, i.e., the (p, q)- Fibonacci and Lucas polynomials, and derived some interesting combinatorial identities for these ...q)-Fibonacci polynomials by applying the famous ...
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REPRESENTING SUMS OF FINITE PRODUCTS OF CHEBYSHEV POLYNOMIALS OF THE FIRST KIND AND LUCAS POLYNOMIALS BY CHEBYSHEV POLYNOMIALS
... cial polynomials, namely Chebyshev polynomials of the second, third and fourth kinds and Fibonacci, Legendre, Laguerre polynomials had been represented by Chebyshev polynomials of all ...
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Fibonacci polynominals of order k, multinomial expansions and probability
... FIBONACCI POLYNOMIALS OF ORDER K, MULTINOMIAL EXPANSIONS AND PROBABILITY ANDREA$ N.. PHILIPPOU Department of Mathematics Unlveristy of Patras Patras, Greece.[r] ...
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A new generalization of convolved (p,q)−Fibonacci and (p,q)−Lucas polynomials
... q)−Lucas polynomials are recursive sequences that generalize several polynomial and number sequences defined by recurrence relations of order two, such as Fibonacci numbers, Lucas numbers, Pell numbers, ...
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Some properties of Fibonacci and Chebyshev polynomials
... Chebyshev polynomials of the first and second kind and those of Fibonacci polynomials and use an elementary method to give Chebyshev polynomials of the first and second kind in terms of ...
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Binomial Transforms of Generalized Fibonacci-Like Sequences
... In addition, some matrices based transforms can be introduced for a given sequence. Binomial transform is one of these transforms and there are also other ones such as rising and falling binomial transforms . Many ...
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FIBONACCI SERIES IN MATHEMATICS
... According to this theory, all the male bees have a single parent whereas there are two parents of a female bee. On tracing the pedigree of the male bee, it is observed that it has 1 parent, 2 grandparents, 3 ...
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A NOTE ON HORADAM HYBRINOMIALS
... new polynomials which are called Horadam ...Horadam polynomials. Thanks to this gen- eralization, we obtain the Fibonacci hybrinomials F H n (x); the Lucas hybrinomials LH n 1 ...
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Fibonacci sequences in groupoids
... of Fibonacci sequences in arbitrary groupoids ...The Fibonacci sequences for several groupoids and for the class of groups as special cases are also ...
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Fibonacci Numbers and Golden Ratio- Teaching through the History of Mathematics
... generalized Fibonacci series mathematical derivation and numerical simulation, we get that electricity network and the set of connections etc, which is the load capacity of the ...
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10. Some series identities for some special classes of Apostol-Bernoulli and Apostol-Euler polynomials related to generalized power and alternating sums
... sum (1.16) and the analogues of the expansions of hyperbolic cotangent and hy- perbolic tangent introduced in [20]. These results extend some known formulas [6, 7, 21]. We conclude this section by giving some identities ...
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Hyperbolic Fibonacci and Lucas Functions, “Golden” Fibonacci Goniometry, Bodnar’s Geometry, and Hilbert’s——Part I Hyperbolic Fibonacci and Lucas Functions and “Golden” Fibonacci Goniometry
... Independently on Stakhov, Tkachenko and Rosin, the Ukrainian researcher Oleg Bodnar came to the same ideas. He has introduced in [4] the so-called “golden” hyperbolic functions, which are different from hyperbol- ic ...
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Search | Preprints
... The Fibonacci and Lucas sequences are very well-known examples of second order recurrence ...The Fibonacci numbers are perhaps most famous for appearing in the rabbit breeding problem, introduced by ...
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On Fibonacci and Lucas Vectors and Quaternions
... the Fibonacci vectors, Lucas vectors and their vector products considering two Fibonacci vectors, two Lucas vectors and one of each ...by Fibonacci and Lucas vectors with respect to Fibonacci ...
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