Special functions MOC

Associated Legendre function

To every Legendre polynomial exist a number of associated Legendre functions defined (by one convention¹) for as fun

and

where naturally for .

Mathematica

The Associated Legendre polynomial may be generated in Wolfram Mathematica with LegendreP[ℓ, m, x].

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Footnotes

1. 2018. Introduction to quantum mechanics, §4.1, p. 135 ↩