Lucas Symbolic Formulae and Generating Functions for Chebyshev Polynomials
نویسندگان
چکیده
منابع مشابه
Generating functions of Chebyshev-like polynomials
In this short note, we give simple proofs of several results and conjectures formulated by Stolarsky and Tran concerning generating functions of some families of Chebyshev-like polynomials.
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In his paper of 2000, Kenneth B. Stolarsky made various observations and conjectures about discriminants and generating functions of certain types of Chebyshev-like polynomials. We prove several of these conjectures. One of our proofs involves Wilf-Zeilberger pairs and a contiguous relation for hypergeometric series.
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We derive a collection of identities for bivariate Fibonacci and Lu-cas polynomials using essentially a matrix approach as well as properties of such polynomials when the variables x and y are replaced by polynomials. A wealth of combinatorial identities can be obtained for selected values of the variables.
متن کاملTutte polynomials of wheels via generating functions
We find an explicit expression of the Tutte polynomial of an $n$-fan. We also find a formula of the Tutte polynomial of an $n$-wheel in terms of the Tutte polynomial of $n$-fans. Finally, we give an alternative expression of the Tutte polynomial of an $n$-wheel and then prove the explicit formula for the Tutte polynomial of an $n$-wheel.
متن کاملIntegral formulas for Chebyshev polynomials and the error term of interpolatory quadrature formulae for analytic functions
We evaluate explicitly the integrals ∫ 1 −1 πn(t)/(r ∓ t)dt, |r| = 1, with the πn being any one of the four Chebyshev polynomials of degree n. These integrals are subsequently used in order to obtain error bounds for interpolatory quadrature formulae with Chebyshev abscissae, when the function to be integrated is analytic in a domain containing [−1, 1] in its interior.
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ژورنال
عنوان ژورنال: Journal of High Energy Physics, Gravitation and Cosmology
سال: 2021
ISSN: 2380-4327,2380-4335
DOI: 10.4236/jhepgc.2021.73052