Calculation of atomic integrals with exponentialy correlated functions

A new type of correlation atomic integrals occurring in variation energy calculations of three-particle Coulomb systems is studied. A integrand in them along with an interparticle distance linear term under an exponent additionally contains a quadratic term. It is demonstrated that these integrals are analytically expressed through Faddeeva function of a pure imaginary argument and its derivatives. A stable and fast algorithm for calculation of Faddeeva function derivatives to the twentieth order is developed. The test values of the studied special functions are provided.