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Analysis in Theory and Applications

, Volume 19, Issue 2, pp 166–184 | Cite as

On Abel-Gontscharoff-Gould’s polynomials

  • He Tianxiao
  • Leetsch C. Hsu
  • Peter J. S. Shiue
Article

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.

Key Words

annihilation coefficients Gould’s identity Abel-Gontscharoff polynomial ring of formal power series Abel-Gontscharoff interpolation series 

AMS(2000) subject classification

05A10 11C08 13F25 41A58 

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Copyright information

© Springer 2003

Authors and Affiliations

  • He Tianxiao
    • 1
  • Leetsch C. Hsu
    • 2
  • Peter J. S. Shiue
    • 3
  1. 1.Department of Mathematics and Computer ScienceIllinois Wesleyan UniversityBloomingtonUSA
  2. 2.Department of MathematicsDalian University of TechnologyDalianP. R. China
  3. 3.Department of MathematicsUniversity of Nevada Las VegasLas VegasUSA

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