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Article
A Symbolic Operator Approach to Several Summation Formulas for Power Series
Journal of Computational and Applied Mathematics (2005)
  • Tian-Xiao He, Illinois Wesleyan University
  • Leetsch C. Hsu, Dalian University of Technology
  • Peter J.-S. Shiue
  • D. C. Torney
Abstract

This paper deals with the summation problem of power series of the form Sba (f; x) = ∑a ≤ k ≤ b f(k) xk, where 0≤ a < b ≤ ∞, and {f(k)} is a given sequence of numbers with k Є [a, b) or f(t) is a differentiable function defined on [a, b). We present a symbolic summation operator with its various expansions, and construct several summation formulas with estimable remainders for Sba (f; x), by the aid of some classical interpolation series due to Newton, Gauss and Everett, respectively.

Keywords
  • Symbolic summation operator,
  • power series,
  • generating function,
  • Eulerian fraction,
  • Eulerian polynomial,
  • Eulerian numbers,
  • Newton’s interpolation,
  • Evertt’s interpolation,
  • Gauss interpolation.
Publication Date
2005
Publisher Statement
The Journal of Computational and Applied Mathematics is published by Elsevier, http://www.journals.elsevier.com/journal-of-computational-and-applied-mathematics/.
Citation Information
Tian-Xiao He, Leetsch C. Hsu, Peter J.-S. Shiue and D. C. Torney. "A Symbolic Operator Approach to Several Summation Formulas for Power Series" Journal of Computational and Applied Mathematics Vol. 177 (2005)
Available at: http://works.bepress.com/tian_xiao_he/4/