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. The relevant radial perturbation equations and formulae for corrections to the energy are derived. For the ground state up to the first order in a magnetic field all the differential equations arising are solved directly to infinite order in relativity. The general solutions of the radial equations are obtained by expansion in appropriate Laguerre polynomials. Exact energy corrections for zeroth and first order as well as very accurate results for second and third order in relativity are presented up to 12 orders in a magnetic field.No biography provided yet