Symbols:P/Legendre Polynomial
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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