In quantum mechanics, the expectation value of a quantity on a quantum state, provided that the state itself gives in the classical limit a motion of a particle in a definite path, in the classical limit goes over to a Fourier series form of the classical quantity. In contrast to this widely accepted point of view, a rigorous calculation shows that the expectation value on such a state in the classical limit exactly gives the Fejer arithmetic mean of the partial sums of the Fourier series.