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Selected Works of Tian-Xiao He
Article
Recursive Sequences and Girard-Waring Identities with Applications in Sequence Transformation
Electronic Research Archive (2020)
  • Tian-Xiao He
  • Peter J.-S. Shiue
  • Zihan Nie
  • Minghao Chen
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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.
Keywords
  • Girard-Waring identity,
  • Binet formula,
  • recursive sequence,
  • divided difference,
  • Chebyshev polynomials
Disciplines
Publication Date
Spring June, 2020
DOI
https://www.aimsciences.org/article/doi/10.3934/era.2020057
Publisher Statement
Electronic Research Archive (ERA) is is a publication of the American Institute of Mathematical Sciences. For more information please visit ERA online.
Citation Information
Tian-Xiao He, Peter J.-S. Shiue, Zihan Nie and Minghao Chen. "Recursive Sequences and Girard-Waring Identities with Applications in Sequence Transformation" Electronic Research Archive Vol. 28 Iss. 2 (2020) p. 1049 - 1062 ISSN: 2688-1594
Available at: http://works.bepress.com/tian_xiao_he/94/