منابع مشابه
A New Class of q-Fibonacci Polynomials
the simple evaluation (3.2 ). This fact led me to a thorough study of this q-analogue via a combinatorial approach based on Morse code sequences. We show that these q-Fibonacci polynomials satisfy some other recurrences too, generalize some well-known facts for ordinary Fibonacci polynomials to this case, derive their generating function and study the special values Fn(1,−q ) and Fn(1,−1) which...
متن کاملNEW CONNECTION FORMULAE BETWEEN (p, q)−FIBONACCI POLYNOMIALS AND CERTAIN JACOBI POLYNOMIALS
The main purpose of this article is to solve the connection problems between (p, q)−Fibonacci polynomials and the two polynomials, namely Chebyshev polynomials of third and fourth kinds which are considered as two nonsymmetric polynomials of the Jacobi polynomials. Moreover, the inversion connection formulae for the latter formulae are given. We show that all the connection coefficients are exp...
متن کاملZeros of a Class of Fibonacci-type Polynomials
with the initial values G0(x) = a and G1(x) = x + b. The polynomials Gn−1(1, 0;x) and Gn(2, 0;x)(n ≥ 1) are just the usual Fibonacci polynomials Fn(x) and the Lucas polynomials Ln(x), respectively. Our concern in this paper is to study some of the properties of the zeros of the Fibonacci-type polynomials Gn(a, b;x). The zeros of Fn(x) and Ln(x) have been given explicitly by V. E. Hoggatt, Jr. a...
متن کاملq-ANALOGS OF GENERALIZED FIBONACCI AND LUCAS POLYNOMIALS
The Fibonacci operator approach inspired by Andrews (2004) is explored to investigate q-analogs of the generalized Fibonacci and Lucas polynomials introduced by Chu and Vicenti (2003). Their generating functions are compactly expressed in terms of Fibonacci operator fractions. A determinant evaluation on q-binomial coefficients is also established which extends a recent result of Sun (2005).
متن کامل-̂fibonacci Polynomials
Let MC be the monoid of all Morse code sequences of dots a(:=®) and dashes b(: = -) with respect to concatenation. MC consists of all words in a and b. Let P be the algebra of all polynomials HveMCK ^h r e a l coefficients. We are interested in: a) polynomials in P which we call abstract Fibonacci polynomials. They are defined by the recursion Fn(a, b) = aF^a, b) + bFn_2(a, b) with initial valu...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2003
ISSN: 1077-8926
DOI: 10.37236/1712