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Open AccessArticle

General Linear Recurrence Sequences and Their Convolution Formulas

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Section of Mathematics, International Telematic University UniNettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
2
Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Largo San Leonardo Murialdo, 1, 00146 Roma, Italy
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Author to whom correspondence should be addressed.
Axioms 2019, 8(4), 132; https://doi.org/10.3390/axioms8040132
Received: 29 September 2019 / Revised: 11 November 2019 / Accepted: 15 November 2019 / Published: 19 November 2019
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 liner recursions; convolution formulas; Gegenbauer polynomials; Humbert polynomials; classical polynomials in several variables; classical number sequences
MDPI and ACS Style

Ricci, P.E.; Natalini, P. General Linear Recurrence Sequences and Their Convolution Formulas. Axioms 2019, 8, 132.

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