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The Wigner d function, which is the essential part of an irreduciblerepresentation of SU(2) and SO(3) parameterized with Euler angles, has beenknow to suffer from a serious numerical errors at high spins, if it iscalculated by means of the Wigner formula as a polynomial of cos and sin ofhalf of the second Euler angle. This paper shows a way to avoid this problem byexpressing the d functions as the Fourier series of the half angle. A precisenumerical table of the coefficients of the series is obtainable from a website.

Analytical formula for numerical evaluations of the Wigner rotation matrices at high spins