Recursive sequences and girard-waring identities with applications in sequence transformation

Tian-Xiao He; Peter J.-S. Shiue; Zihan Nie; Minghao Chen; Tian-Xiao He; Peter J.-S. Shiue; Zihan Nie; Minghao Chen

doi:10.3934/era.2020057

Electronic Research Archive

2020, Volume 28, Issue 2: 1049-1062. doi: 10.3934/era.2020057

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Recursive sequences and girard-waring identities with applications in sequence transformation

1.
Department of Mathematical Sciences, University of Nevada, Las Vegas, Las Vegas, Nevada, 89154-4020, USA
2.
Department of Mathematics, Illinois Wesleyan University, Bloomington, Illinois 61702, USA

Received: 01 January 2020 Revised: 01 May 2020
Primary: 05A15; Secondary: 05A05, 15B36, 15A06, 05A19, 11B83

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.
- Girard-Waring identity,
- Binet formula,
- recursive sequence,
- divided difference,
- Chebyshev polynomials
Citation: Tian-Xiao He, Peter J.-S. Shiue, Zihan Nie, Minghao Chen. Recursive sequences and girard-waring identities with applications in sequence transformation[J]. Electronic Research Archive, 2020, 28(2): 1049-1062. doi: 10.3934/era.2020057

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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.

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