A GENERALIZATION OF BESSEL’S INTEGRAL FOR THE BESSEL COEFFICIENTS

Abstract

We derive an integral over the m-dimensional unit hypercube that generalizes Bessel’s integral for Jn(x). The integrand is G(xψ(t)) exp(−2π i n · t), where G is analytic, and ψ(t) =e2πit1+. . .+e2πitm+e−2πi(t1+...+tm), while n is a set of non-negative integers. In particular, we consider the case when G is a hypergeometric function pFq.