Bounds for the Appell Function F2

The exact matrix elements for certain second order radiation processes in hydrogenic atoms can all be expressed in terms of a certain generalized hypergeometric function of two variables. In this paper we obtain bounds for this function as the two variables tend to the singular point z = 1 from the upper half plane. The bounds are shown to he uniform in the hypergeometric parameters in the ranges of interest, and may he used to bound the exact matrix elements in both the non-relativistic and relativistic cases.