# Legendre functions

From Encyclopedia of Mathematics

Functions that are solutions of the Legendre equation

(*) |

where and are arbitrary numbers. If and , then the solutions of equation (*), restricted to , are called Legendre polynomials; for integers with , the solutions of equation (*), restricted to , are called Legendre associated functions.

#### Comments

#### References

[a1] | M. Abramowitz, I.A. Stegun, "Handbook of mathematical functions" , Dover, reprint (1965) pp. Chapt. 8 |

[a2] | N.N. Lebedev, "Special functions and their applications" , Dover, reprint (1972) (Translated from Russian) |

**How to Cite This Entry:**

Legendre functions.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Legendre_functions&oldid=15230

This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article