Abstract
We extend a technique recently introduced by Chen Zhuoyu and Qi Lan in order to find convolution formulas for second order linear recurrence polynomials generated by 1 1 + a t + b t 2 x . The case of generating functions containing parameters, even in the numerator is considered. Convolution formulas and general recurrence relations are derived. Many illustrative examples and a straightforward extension to the case of matrix polynomials are shown.
Highlights
Generating functions [1] constitute a bridge between continuous analysis and discrete mathematics
We extend a technique recently introduced by Chen Zhuoyu and Qi Lan in order to find x convolution formulas for second order linear recurrence polynomials generated by 1+at1+bt2
In a recent article Chen Zhuoyu and Qi Lan [9] introduced convolution formulas for second order linear recurrence sequences related to the generating function [1] of the type f (t) =
Summary
Generating functions [1] constitute a bridge between continuous analysis and discrete mathematics. We recall the Chebyshev polynomials of the first and second kind, which are powerful tools used in both theoretical and applied mathematics Their links with the Lucas and Fibonacci polynomials have been studied and many properties have been derived. The important calculation of sums of several types of polynomials have been recently studied (see e.g., [3,4,5] and the references therein) This kind of subject has attracted many scholars. In a recent article Chen Zhuoyu and Qi Lan [9] introduced convolution formulas for second order linear recurrence sequences related to the generating function [1] of the type f (t) =. In the last section the results are extended, in a straightforward way, to the case of matrix polynomials
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