Definition:Associated Legendre Function
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Definition
The associated Legendre functions are the real functions defined and denoted as:
- $\map { {P_n}^m} x = \paren {1 - x^2}^{m / 2} \dfrac {\d^m} {\d x^m} \map {P_n} x$
where $\map {P_n} x$ is the Legendre polynomial of order $n$.
The associated Legendre functions are the solutions to Legendre's associated differential equation.
Also see
- Results about the associated Legendre functions can be found here.
Source of Name
This entry was named for Adrien-Marie Legendre.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Legendre's differential equation
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Legendre's differential equation