Recursive Sequences and Girard-Waring Identities with Applications in Sequence Transformation

Authors

Tian-Xiao He, Illinois Wesleyan University
Peter J.-S. Shiue, University of Nevada, Las VegasFollow
Zihan Nie, Illinois Wesleyan University
Minghao Chen, Illinois Wesleyan University

Document Type

Article

Publication Date

6-1-2020

Publication Title

Electronic Research Archive

Volume

28

Issue

2

First page number:

1049

Last page number:

1062

Abstract

We present here a generalized Girard-Waring identity constructed from recursive sequences. We also present the construction of Binet Girard-Waring identity and classical Girard-Waring identity by using the generalized Girard-Waring identity and divided differences. The application of the generalized Girard-Waring identity to the transformation of recursive sequences of numbers and polynomials is discussed.

Keywords

Girard-Waring identitiy; Binet formula; Recursive sequence; Divided difference; Chebyshev polynomials

Disciplines

Applied Mathematics

Language

English

Repository Citation

He, T., Shiue, P. J., Nie, Z., Chen, M. (2020). Recursive Sequences and Girard-Waring Identities with Applications in Sequence Transformation. Electronic Research Archive, 28(2), 1049-1062.
http://dx.doi.org/10.3934/era.2020057