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Gaussian Integrals, Multinomial Coefficients, and Homogeneous Functions

✍ Scribed by Sergio Venturini

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
55 KB
Volume
22
Category
Article
ISSN
0196-8858

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✦ Synopsis

The purpose of this work is to describe some links between the ap-. parently unrelated objects named in the title of the paper. Let us give a short description of them.

Gaussian Integrals. The classical Gaussian integral is

yϱ 2 yx r2 ' e dxs 2 . H yϱ Moreover, if A is an n = n symmetric positive definite matrix, then n ' 2 Ž . y² A x, x : r2 e d xs . H n ' det A ‫ޒ‬ Ž . Multinomial Coefficients. Let us recall that the Euler function ⌫ x is a function such that for x G 0, qϱ uy 1 yu ⌫ x s x e du,

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