# Difference between revisions of "Legendre polynomials"

Carl McBride (talk | contribs) |
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==See also== | ==See also== | ||

+ | *[[Associated Legendre function]] | ||

*[http://mathworld.wolfram.com/LegendrePolynomial.html Legendre Polynomial -- from Wolfram MathWorld] | *[http://mathworld.wolfram.com/LegendrePolynomial.html Legendre Polynomial -- from Wolfram MathWorld] | ||

[[category: mathematics]] | [[category: mathematics]] |

## Revision as of 12:00, 20 June 2008

**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*.