Work

Overview of Six Number/Polynomial Sequences Defined by Quadratic Recurrence Relations

Year: 2025

Type: article

Abstract: Six well-known sequences (Fibonacci and Lucas numbers, Pell and Pell–Lucas polynomials, and Chebyshev polynomials) are characterized by quadratic linear recurrence relations. They are unified and reviewed under a common framework. Several useful properties (such as Binet-form expressions, Cassini identities, and Catalan formulae) and remarkable results concerning power sums, ordinary convolutions, and binomial convolutions are presented by employing the symmetric feature, series rearrangements, and the generating function approach. Most of the classical results concerning these six number/polynomial sequences are recorded as consequences.

Source: Symmetry

DOI: 10.3390/sym17050714

Authors: Yujie Kang, Marta Na Chen, Wenchang Chu

Institution: Zhoukou Normal University

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Zhoukou Normal University