Some definite integrals of the product of two Bessel functions of the second kind: (order zero)

Abstract

A new integral representation is derived for the expression J 0 ( z ) J 0 ( Z ) + Y 0 ( z ) ⋅ Y 0 ( Z ) {J_0}(z){J_0}(Z) + {Y_0}(z) \cdot {Y_0}(Z) and used to evaluate a number of integrals containing Y 0 ( a x ) Y 0 ( b x ) {Y_0}(ax){Y_0}(bx) . A supplementary table of integrals involving the function K 0 ( x ) {K_0}(x) in the integrand appears in the microfiche section of this issue.