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Expansions for Repeated Integrals of Products with Applications to the Multivariate Normal

Expansions for Repeated Integrals of Products with Applications to the Multivariate Normal

We extend Leibniz' rule for repeated derivatives of a product to multivariate integrals of a product. As an application we obtain expansions for P(a < Y < b) for Y ~ Np(0,V) and for repeated integrals of the density of Y. When V−1y > 0 in R3 the expansion for …