Numerical properties of the convolution theorems of B functions

For the computation of convolution integrals of B functions [Eq. (2.14) of E. Filter and E. O. Steinborn, Phys. Rev. A 18, 1 (1978)] which are a special class of exponential-type functions, different analytic representations are available. We have investigated the numerical properties of these convolution formulas and found out that results of sufficient accuracy can be obtained for molecular calculations. We have also investigated the numerical properties of the corresponding one-center integrals. Some new mathematical properties of B functions that are essential for the understanding of the numerical properties of the convolution formulas are derived.