  The Shapiro--Wilk test (SW) and the Anderson--Darling test (AD) turned out to
be strong procedures for testing for normality. They are joined by a class of
tests for normality proposed by Epps and Pulley that, in contrary to SW and AD,
have been extended by Baringhaus and Henze to yield easy-to-use affine
invariant and universally consistent tests for normality in any dimension. The
limit null distribution of the Epps--Pulley test involves a sequences of
eigenvalues of a certain integral operator induced by the covariance kernel of
the limiting Gaussian process. We solve the associated integral equation and
present the corresponding eigenvalues.
