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Fourier-Budan Theorem


For any real alpha and beta such that beta>alpha, let p(alpha)!=0 and p(beta)!=0 be real polynomials of degree n, and v(x) denote the number of sign changes in the sequence {p(x),p^'(x),...,p^((n))(x)}. Then the number of zeros in the interval [alpha,beta] (each zero counted with proper multiplicity) equals v(alpha)-v(beta) minus an even nonnegative integer.


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References

Henrici, P. Applied and Computational Complex Analysis, Vol. 1: Power Series-Integration-Conformal Mapping-Location of Zeros. New York: Wiley, p. 443, 1988.

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Fourier-Budan Theorem

Cite this as:

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

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