#### 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.

#### Disciplines

Applied Mathematics | Mathematics

#### Recommended Citation

He, Tian-Xiao; Hsu, Leetsch; Shiue, Peter; and Torney, D., "A Symbolic Operator Approach to Several Summation Formulas for Power Series" (2005). *Scholarship*. 14.

https://digitalcommons.iwu.edu/math_scholarship/14

## Comments

The

Journal of Computational and Applied Mathematicsis published by Elsevier, http://www.journals.elsevier.com/journal-of-computational-and-applied-mathematics/.