Lukács Theorem

Let be an th degree polynomial which is nonnegative in . Then can be represented in the form

${[A(x)]^2+(1-x^2)[B(x)]^2 for m even; (1+x)[C(x)]^2+(1-x)[D(x)]^2 for m odd,$

(1)

where , , , and are real polynomials whose degrees do not exceed .

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References

Szegö, G. Orthogonal Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., p. 4, 1975.

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Lukács Theorem

Cite this as:

Weisstein, Eric W. "Lukács Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LukacsTheorem.html

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