DocServer

Advances in the theory of box integrals

Bailey, David H. and Borwein, Jonathan M. and Crandall, Richard E. (2010) Advances in the theory of box integrals. Mathematics of Computation, 79 . pp. 1839-1866.

[img]
Preview
PDF
Download (319Kb) | Preview

    Abstract

    Box integrals, being expectations such as $\langle |\vec r|^s \rangle$ or $\langle |\vec r - \vec q|^s \rangle$ with $\vec r, \vec q$ chosen randomly over the unit $n$-cube, have over the years been given closed forms for certain $n, s$. By employing experimental mathematics together with a new analytic strategy, we have been able to prove that for $n = 1,2,3$ dimensions, and any integer $s$, the box integrals are ``hypergeometrically closed," in a sense we clarify herein. We are also able to supply a compendium of new, exact box-integral evaluations that arise naturally from the theory.

    Item Type: Article
    Additional Information: pubdom FALSE
    Subjects: 65-xx Numerical analysis
    Faculty: UNSPECIFIED
    Depositing User: lingyun ye
    Date Deposited: 30 Mar 2009
    Last Modified: 05 Jan 2015 15:55
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/389

    Actions (login required)

    View Item