Legendre polynomials: Difference between revisions

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(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...)
 
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'''Legendre polynomials''' (aka. Legendre functions of the first kind, Legendre coefficients, or zonal harmonics)
'''Legendre polynomials''' (aka. Legendre functions of the first kind, Legendre coefficients, or zonal harmonics)
are solutions of the [[Legendre differential equation]]].
are solutions of the [[Legendre differential equation]].
The Legendre polynomial, <math>P_n (z)</math> can be defined by the contour integral
The Legendre polynomial, <math>P_n (z)</math> can be defined by the contour integral



Revision as of 18:04, 30 May 2007

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.