Integral Reduction Arising in Double Transfer and Excitation Amplitude

The purpose of this article is to develop an integral derived from the double transfer and excitation theory. The reduced form of this integral, so obtained, can serve in the computation of the transition amplitude which is from numerical point of view difficult to implement. This amplitude is of great interest in the resonant and non resonant transfer and excitation (RTE and NTE) processes. (atomic and molecular physics)