A symbolic operator approach to several summation formulas for power series II

This paper deals with the summation problem of power series of the form Sb a(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 Sb a(f ;x), by the aid of some classical interpolation series due to Newton, Gauss and Everett, respectively. AMS Subject Classification: 65B10, 39A70, 41A80, 05A15.