A Symbolic Operator Approach to Several Summation Formulas for Power Series

Tian-Xiao He, Leetsch C. Hsu, Peter J.-S. Shiue, D. C. Torney

Research output: Journal ArticleArticlepeer-review

Abstract

<p> This paper deals with the summation problem of power series of the form Sba (f; x) = &sum;a &le; k &le; b f(k) xk, where 0&le; a &lt; b &le; &infin;, and {f(k)} is a given sequence of numbers with k &Jukcy; [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.</p>
Original languageAmerican English
JournalJournal of Computational and Applied Mathematics
Volume177
StatePublished - 2005

Keywords

  • Symbolic summation operator
  • power series
  • generating function
  • Eulerian fraction
  • Eulerian polynomial
  • Eulerian numbers
  • Newton’s interpolation
  • Evertt’s interpolation
  • Gauss interpolation.

Disciplines

  • Applied Mathematics
  • Mathematics

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