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By using the plane-wave expansion for the electromagnetic-field vectorpotential, transition matrix elements between the relativistic bound andunbound states of hydrogenic atoms were expressed explicitly in terms of finiteseries made of hypergeometric functions. This representation for the abovementioned matrix elements proved very convenient for direct numericalcalculation of their contributions to the Lamb shift in hydrogenic atoms.

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