A program to compute exact hydrogenic radial integrals, oscillator strengths, and Einstein coefficients, for principal quantum numbers up to image Original Research Article

An exact expression for the dipole radial integral of hydrogen has been given by Gordon [Ann. Phys. 2 (1929) 1031]. It contains two hypergeometric functions image, which are difficult to calculate directly, when the (negative) integers a, b are large, as in the case of high Rydberg states of hydrogenic ions. We have derived a simple method [D. Hoang-Binh, Astron. Astrophys. 238 (1990) 449], using a recurrence relation to calculate exactly F, starting from two initial values, which are very easy to compute. We present here a numerical code using this method.