On sequences of numbers and polynomials defined by linear recurrence relations of order 2
type: Item
instance of: scholarly article
title: On sequences of numbers and polynomials defined by linear recurrence relations of order 2
zbMATH Open document ID: 1193.11014
DOI: 10.1155/2009/709386
author: Tian-Xiao He
author: Peter J.-S. Shiue
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2009-11-10T00:00:00Z
full work available at URL: https://eudml.org/doc/45736
review text: Summary: Here we present a new method to construct the explicit formula of a sequence of numbers and polynomials generated by a linear recurrence relation of order 2. The applications of the method to the Fibonacci and Lucas numbers, Chebyshev polynomials, the generalized Gegenbauer-Humbert polynomials are also discussed. The derived idea provides a general method to construct identities of number or polynomial sequences defined by linear recurrence relations. The applications using the method to solve some algebraic and ordinary differential equations are presented.
Mathematics Subject Classification ID: 11B39
Mathematics Subject Classification ID: 11C08
zbMATH DE Number: 5627902
Wikidata QID: Q58648503
MaRDI profile type: Publication
OpenAlex ID: W1975938117
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description: scientific article; zbMATH DE number 5627902