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单词 Kac Formula
释义

Kac Formula

The expected number of Real zeros of a Random Polynomial of degree is

(1)
 (2)

As ,
(3)

where


(4)

The initial term was derived by Kac (1943).


References

Edelman, A. and Kostlan, E. ``How Many Zeros of a Random Polynomial are Real?'' Bull. Amer. Math. Soc. 32, 1-37, 1995.

Kac, M. ``On the Average Number of Real Roots of a Random Algebraic Equation.'' Bull. Amer. Math. Soc. 49, 314-320, 1943.

Kac, M. ``A Correction to `On the Average Number of Real Roots of a Random Algebraic Equation'.'' Bull. Amer. Math. Soc. 49, 938, 1943.


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