# Favard theorem

From Encyclopedia of Mathematics

*on orthogonal systems*

If the following recurrence relation holds for real numbers and :

then there is a function of bounded variation such that

It was established by J. Favard [1]. Sometimes this result is also linked with the name of J. Shohat.

#### References

[1] | J. Favard, "Sur les polynomes de Tchebicheff" C.R. Acad. Sci. Paris , 200 (1935) pp. 2052–2053 |

[2] | G. Szegö, "Orthogonal polynomials" , Amer. Math. Soc. (1975) |

**How to Cite This Entry:**

Favard theorem.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Favard_theorem&oldid=11205

This article was adapted from an original article by Yu.N. Subbotin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article