Separation Theorem
There exist numbers 
, 
, 
, such that
where
, 2, ..., 
, 
and 
. Furthermore, the zeros 
, ..., 
, arranged in increasingorder, alternate with the numbers 
, ...
, so
More precisely,
for
, ..., 
.See also Poincaré Separation Theorem, Sturmian Separation Theorem
References
Szegö, G. Orthogonal Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., p. 50, 1975.