The singular integral is calculated numerically is the Bessel function of order i, by using an integral expression for . If f(x) is bounded and analytic in some complex domain, the double integral obtained in this way is calculated for
by Gauss-Laguerre and Gauss-Chebyshev
by Gauss-Laguerre formulae, changes of variables,
and Gauss-Legendre formulae. The bound 1.5 is searched by trial. Further the singular integral is derived from S. It is stated that the FORTRAN subroutines run very fast and give a relative precision better than (for all ).