Category:Examples of Legendre Polynomials

This category contains examples of Legendre Polynomial.

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 $\map {P_n} x$.