Torney, A symbolic operator approach to several summation formulas for power series

This paper deals with the summation problem of power series of the form Sba(f;x) = a≤k≤b f(k)x k, where 0 ≤ a < b ≤ ∞, and {f(k)} is a given sequence of numbers with k ∈ [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