A symbolic operator approach to several summation formulas for power series

Authors:
T. X. He;L. C. Hsu;P. J.-S. Shiue;D. C. Torney
Affiliations:
Department of Mathematics and Computer Science, Illinois Wesleyan University, Bloomington, IL;Department of Mathematics, Dalian University of Technology, Dalian 116024, P.R. China;Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, NV;Theoretical Division, Los Alamos National Lab, MS K710, Los Alamos, NM
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

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Abstract

This paper deals with the summation problem of power series of the form Sab(f;x) = Σa ≤ k ≤ b f(k)xk, 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 Sab(f;x), by the aid of some classical interpolation series due to Newton, Gauss and Everett, respectively.