Wacker Art Legendre Polynomials
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## Mathematical Functions - Legendre Polynomials

Definition of the Legendre polynomial Pn(x).

Even or odd Legendre polynomials.

Rodrigues formular for Legendre polynomials.

The Legendre polynomials are solutions of the Legendre differential equation.

Executing the derivative d/dx will result in the following differential equation:

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### P11 = (88179x11 - 230945x9 + 218790x7 - 90090x5 + 15015x3 - 693x)/256

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## Legendre Functions of the Second Kind

Recusive Definition:

 Q4 Q5
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## Associated Legendre Polynomials

The associated Legendre polynomials are defined with the help of the derivatives of the Legendre polynomials as follows:

m = 0 .. l

The Pl(x) are the Legendre polynomials.

The Pl(0)(x) of the associated Legendre polynomials are the normal Legendre polynomials.

Inserting Rodrigues formular:

will result in the following expression for the associated Legendre polynomials:

The associated Legendre polynomials for negative m are then defined by

The value of m can now be the range -l..m..l.

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27. März 2021 Version 2.0
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