# Legendre polynomials

Revision as of 18:04, 30 May 2007 by Carl McBride (talk | contribs) (New page: '''Legendre polynomials''' (aka. Legendre functions of the first kind, Legendre coefficients, or zonal harmonics) are solutions of the Legendre differential equation]. The Legendre pol...)

**Legendre polynomials** (aka. Legendre functions of the first kind, Legendre coefficients, or zonal harmonics)
are solutions of the Legendre differential equation].
The Legendre polynomial, can be defined by the contour integral

The first seven Legendre polynomials are:

"shifted" Legendre polynomials (which obey the orthogonality relationship):

Powers in terms of Legendre polynomials:

Associated Legendre polynomials.

*etc*.