Abstract
<p> 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.</p>
Original language | American English |
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Journal | Journal of Computational and Applied Mathematics |
Volume | 177 |
State | Published - 2005 |
Keywords
- Eulerian fraction
- Eulerian numbers
- Eulerian polynomial
- Evertt’s interpolation
- Gauss interpolation.
- Newton’s interpolation
- Symbolic summation operator
- generating function
- power series
Disciplines
- Applied Mathematics
- Mathematics