Asymptotic expansion of a quadruple integral involving a Bessel function

摘要

An asymptotic expansion is derived for a quadruple integral involving the Bessel function J0[λ(xy + zw)], where each of the integration variables x, y, z and w belongs to the interval [0, 1] and the large variable λ tends to infinity. Corresponding results are also obtained for similar integrals in two and three dimensions.