Computationally efficient analytic representation of relativistic transition matrix elements in the Lamb shift calculations for hydrogenic atoms

By using the plane-wave expansion for the electromagnetic-field vector potential, transition matrix elements between the relativistic bound and unbound states of hydrogenic atoms were expressed explicitly in terms of finite series made of hypergeometric functions. This representation for the above mentioned matrix elements proved very convenient for direct numerical calculation of their contributions to the Lamb shift in hydrogenic atoms.