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.

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.