The separation theorem states that there exist numbers , , , such that
|
(1)
|
where ,
2, ..., ,
and .
Furthermore, the zeros , ..., , arranged in increasing order, alternate with the numbers
,
...,
so
|
(2)
|
More precisely,
|
(3)
|
for ,
..., .
See also
Poincaré Separation
Theorem,
Sturmian Separation Theorem
Explore with Wolfram|Alpha
References
Szegö, G. Orthogonal Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., p. 50, 1975.Referenced
on Wolfram|Alpha
Separation Theorem
Cite this as:
Weisstein, Eric W. "Separation Theorem."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SeparationTheorem.html
Subject classifications