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

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

doi:10.3934/era.2020057

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

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

Illinois Wesleyan University

Research output: Journal Article › Article › peer-review

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.

Original language	American English
Journal	Electronic Research Archive
Volume	28
DOIs	https://doi.org/10.3934/era.2020057
State	Published - Jun 2020

Keywords

Binet formula
Chebyshev polynomials
Girard-Waring identity
divided difference
recursive sequence

Disciplines

Applied Mathematics
Mathematics

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10.3934/era.2020057License: Unspecified

Cite this

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title = "Recursive Sequences and Girard-Waring Identities with Applications in Sequence Transformation",

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 = "Binet formula, Chebyshev polynomials, Girard-Waring identity, divided difference, recursive sequence",

author = "Tian-Xiao He and Shiue, \{Peter J.-S.\} and Zihan Nie and Minghao Chen",

note = "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.",

year = "2020",

month = jun,

doi = "10.3934/era.2020057",

language = "American English",

volume = "28",

journal = "Electronic Research Archive",

}

TY - JOUR

T1 - Recursive Sequences and Girard-Waring Identities with Applications in Sequence Transformation

AU - He, Tian-Xiao

AU - Shiue, Peter J.-S.

AU - Nie, Zihan

AU - Chen, Minghao

N1 - 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.

PY - 2020/6

Y1 - 2020/6

N2 - 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.

AB - 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.

KW - Binet formula

KW - Chebyshev polynomials

KW - Girard-Waring identity

KW - divided difference

KW - recursive sequence

UR - https://www.aimsciences.org/article/doi/10.3934/era.2020057

U2 - 10.3934/era.2020057

DO - 10.3934/era.2020057

M3 - Article

VL - 28

JO - Electronic Research Archive

JF - Electronic Research Archive

ER -

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

Abstract

Keywords

Disciplines

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