Symbols:P/Associated Legendre Function of the First Kind

Associated Legendre Function of the First Kind

$\map { {P_n}^m} x$

Let $m, n \in \Z_{\ge 0}$ be non-negative integers.

The associated Legendre functions of the first kind 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 $\LaTeX$ code for \(\map { {P_n}^m} x\) is \map { {P_n}^m} x .

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