On a simple relation between hydrogenic radial matrix elements

A simple relation between hydrogen radial matrix elements (nl' mod r k-1 mod nl) and (nl' mod r -k-2 mod nl) (l'+l>or=k>or= mod l'-l mod ), previously obtained by Blanchard (1974), is derived more directly from the classical properties of generalised hypergeometric functions and discussed with reference to the SO(2,1) dynamical group of the hydrogen atom. This is an extension of a corresponding result for matrix elements diagonal in the angular momentum quantum number, first derived by Pasternack.