Favard'S Theorem

(Theory)

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What is Favard's theorem?

In mathematics, Favard's theorem, also called the Shohat–Favard theorem, states that a sequence of polynomials satisfying a suitable 3-term recurrence relation is a sequence of orthogonal polynomials. The theorem was introduced in the theory of orthogonal polynomials by Favard and , though essentially the same theorem was used by Stieltjes in the theory of continued fractions many years before Favard's paper, and was rediscovered several times by other authors before Favard's work.

Technology Types

functionmathematical relationorthogonal polynomialpolynomialpropositionstatementtheoremtheorems in approximation theorytheory

Synonyms

Favard theoremFavard-Shohat theoremFavard–Shohat theoremShohat theoremShohat-Favard theoremShohat–Favard theoremShohat's theorem

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