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
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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
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