Identities For Linear Recursive Sequences Of Order 2

Document Type

Article

Publication Date

7-22-2021

Publication Title

Electronic Research Archive

Volume

29

Issue

5

First page number:

3489

Last page number:

3507

Abstract

We present here a general rule of construction of identities for recursive sequences by using sequence transformation techniques developed in [16]. Numerous identities are constructed, and many well known identities can be proved readily by using this unified rule. Various Catalan-like and Cassini-like identities are given for recursive number sequences and recursive polynomial sequences. Sets of identities for Diophantine quadruple are shown.

Keywords

Balancing numbers; Balancing polynomials; Cassini-like identity; Catalan-like identity; Chebyshev polynomials of the first kind; Chebyshev polynomials of the second kind; Diophantine quadruple; Fermat numbers; Fermat polynomials; Fibonacci numbers; Girard-waring identities; Lucas numbers; Lucas polynomials; Pell numbers; Pell polynomials; Pell-lucas polynomials; Recursive sequence

Disciplines

Statistical, Nonlinear, and Soft Matter Physics

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