Journal of Statistical Physics, Vol. 24, No. 3, 1981. p. 413-418.
The probability density function of the single eigenvalue is expanded in terms of the reciprocal of the dimension of the matrix using Bessel functons. It is shown that for the new matrix ensembles this expansion gives Wigner's semicircle centered at the mean value of the matrix elements plus terms of the order of N^(-1), where N is the dimension of the matrix.