FORMULATION OF SOME GAUSSIAN INTEGRALS OVER R(N) VIA GENERATING-FUNCTIONS

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ERGENC T., DEMIRALP M.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, vol.54, pp.239-248, 1994 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 54
• Publication Date: 1994
• Doi Number: 10.1080/00207169408804355
• Journal Name: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.239-248
• Middle East Technical University Affiliated: No

Abstract

This paper deals with the analytic formulation of the integrals over R(n) with the weight function exp(x(T)Cx) where the integrand is the product of quadratic forms x(T) A(j)x, j = 1,...,p, for arbitrary n x n symmetric matrices A(j). The technique is based on generating functions. First some functions are defined to generate these integrals for the special case A(j) = A(j) = A...A, and then practical formulas for the general case are derived.