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On Abel-Gontscharoff-Gould's polynomials
Analysis in Theory and Applications (2003)
  • Tian-Xiao He, Illinois Wesleyan University
  • Leetsch C. Hsu, Dalian University of Technology
  • Peter J.-S. Shiue
Abstract

In this paper a connective study of Gould’s annihilation coefficients and Abel-Gontscharoff polynomials is presented. It is shown that Gould’s annihilation coefficients and Abel-Gontscharoff polynomials are actually equivalent to each other under certain linear substitutions for the variables. Moreover, a pair of related expansion formulas involving Gontscharoff’s remainder and a new form of it are demonstrated, and also illustrated with several examples.

Keywords
  • Annihilation coefficients,
  • Gould’s identity,
  • Abel-Gontscharoff polynomial,
  • ring of formal power series,
  • Abel-Gontscharoff interpolation series.
Publication Date
2003
Publisher Statement
Analysis in Theory and Applications is published by the Department of Education of Jiangsu Province and Nanjing University, http://www.global-sci.org/ata/.
Citation Information
Tian-Xiao He, Leetsch C. Hsu and Peter J.-S. Shiue. "On Abel-Gontscharoff-Gould's polynomials" Analysis in Theory and Applications Vol. 19 (2003)
Available at: http://works.bepress.com/tian_xiao_he/12/