Convergence of the summation formulas constructed by using a symbolic operator approach

Authors:
Tian-Xiao He;Leetsch C. Hsu;Peter J. -S. Shiue
Affiliations:
-;-;-
Venue:
Computers & Mathematics with Applications
Year:
2006

Citing 2
Cited 1

On certain summation problems and generalizations of Eulerian polynomials and numbers

Discrete Mathematics - Special issue on selected papers in honor of Henry W. Gould
A symbolic operator approach to several summation formulas for power series

Journal of Computational and Applied Mathematics

Symbolization of generating functions; an application of the Mullin-Rota theory of binomial enumeration

Computers & Mathematics with Applications

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Abstract

This paper deals with the convergence of the summation of power series of the form @S@a@?@k(@k)@g^@k, where 0 @? @a @? b @? ~, and { (@k)} is a given sequence of numbers with @k @e (@a, b) or(t) a differentiable function defined on (a, b). Here, the summation is found by using the symbolic operator approach shown in [1]. We will give a different type of the remainder of the summation formulas. The convergence of the corresponding power series will be determined consequently. Several examples such as the generalized Euler's transformation series will also be given. In addition, we will compare the convergence of the given series transforms.