The standard summation operator, the Euler-Maclaurin sum formula, and the Laplace transformation-Reference-Cited by-同舟云学术

The standard summation operator, the Euler-Maclaurin sum formula, and the Laplace transformation

Published:1985-12 Issue:3 Volume:39 Page:367-390
ISSN:0263-6115
Container-title:Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
language:en
Short-container-title:J Aust Math Soc A

Author:

Miller John Boris

Abstract

AbstractA proof is given of the Euler-Maclaurin sum formula, on a Banach space of differentiable vector-valued functions of bounded exponential growth, using the Laplace transformation. Some related summation formulae are proved by the same methods. Properties of the standard summation operator are proved, namely spectral properties and boundedness, continuity and differentiability results.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics,Statistics and Probability

Reference11 articles.

1. Series like Taylor's series

2. The Euler-Maclaurin sum formula for a closed derivation

3. The Euler–Maclaurin formula generated by a summation operator

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