Symbols:P/Legendre Polynomial

Legendre Polynomial of Order $n$

$\map {P_n} x$

Consider the Legendre's differential equation:

$(1): \quad \paren {1 - x^2} \dfrac {\d^2 y} {\d x^2} - 2 x \dfrac {\d y} {\d x} + n \paren {n + 1} y = 0$

for $n \in \N$.

The solutions to $(1)$ are called the Legendre polynomials of order $n$ and denoted $\map {P_n} x$.

The $\LaTeX$ code for \(\map {P_n} x\) is \map {P_n} 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