Asymptotic properties of B -splines, Eulerian numbers and cube slicing

In this paper, we clarify the connections among B -splines, Eulerian numbers and cube slicing. We first show that the asymptotic formula for Eulerian numbers can be considered as a special case of the asymptotic properties of B -splines. The volume of cube slicing can be considered as a value of box...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2011-10, Vol.236 (5), p.988-995
Main Authors: Xu, Yan, Wang, Ren-hong
Format: Article
Language:English
Subjects:
[formula omitted]-splines
Asymptotic approximation
Asymptotic properties
Cube slicing
Cubes
Eulerian numbers
Joints
Mathematical analysis
Mathematical models
Probabilistic methods
Slicing
Splines
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Summary:In this paper, we clarify the connections among B -splines, Eulerian numbers and cube slicing. We first show that the asymptotic formula for Eulerian numbers can be considered as a special case of the asymptotic properties of B -splines. The volume of cube slicing can be considered as a value of box spline functions. Based on the connection, a very simple proof for Laplace and Pólya’s formulas, which were settled by probabilistic methods, is given by spline theory.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2011.08.003