General Linear Recurrence Sequences and Their Convolution Formulas

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.

Keywords

• liner recursions
• convolution formulas
• gegenbauer polynomials
• humbert polynomials
• classical polynomials in several variables
• classical number sequences