On the Distribution of Normal Point Groups.

The system X1, X2, . . ., Xx is called by Fejér2 the conjugate point system of xI , x2, . . ., x, . If all the Xi are outside -1, +1, Fejér calls the point group normal . He pointed out that the roots of many of the classical polynomials are normal, e.g ., the roots of the Tchebicheff and Legendre polynomials . Fejér' proved that if xI, x2, . . . x,, is a normal point group then lim(xi + I xi) = 0. Turán and I 4 improved this to