Next Article in Journal
On Maximal Elements with Applications to Abstract Economies, Fixed Point Theory and Eigenvector Problems
Next Article in Special Issue
Some Identities of Ordinary and Degenerate Bernoulli Numbers and Polynomials
Previous Article in Journal
Face Recognition with Triangular Fuzzy Set-Based Local Cross Patterns in Wavelet Domain
Previous Article in Special Issue
On r-Central Incomplete and Complete Bell Polynomials
Open AccessArticle

Some Convolution Formulae Related to the Second-Order Linear Recurrence Sequence

by Zhuoyu Chen 1 and Lan Qi 2,*
1
School of Mathematics, Northwest University, Xi’an 710127, China
2
School of Mathematics and Statistics, Yulin University, Yulin 719000, China
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(6), 788; https://doi.org/10.3390/sym11060788
Received: 9 May 2019 / Revised: 10 June 2019 / Accepted: 12 June 2019 / Published: 13 June 2019
(This article belongs to the Special Issue Current Trends in Symmetric Polynomials with Their Applications Ⅱ)
The main aim of this paper is that for any second-order linear recurrence sequence, the generating function of which is f ( t ) = 1 1 + a t + b t 2 , we can give the exact coefficient expression of the power series expansion of f x ( t ) for x R with elementary methods and symmetry properties. On the other hand, if we take some special values for a and b, not only can we obtain the convolution formula of some important polynomials, but also we can establish the relationship between polynomials and themselves. For example, we can find relationship between the Chebyshev polynomials and Legendre polynomials. View Full-Text
Keywords: Fibonacci numbers; Lucas numbers; Chebyshev polynomials; Legendre polynomials; Jacobi polynomials; Gegenbauer polynomials; convolution formula Fibonacci numbers; Lucas numbers; Chebyshev polynomials; Legendre polynomials; Jacobi polynomials; Gegenbauer polynomials; convolution formula
MDPI and ACS Style

Chen, Z.; Qi, L. Some Convolution Formulae Related to the Second-Order Linear Recurrence Sequence. Symmetry 2019, 11, 788.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop