Legendre Polynomial/Examples

Examples

The first five Legendre polynomials are:

$\map {P_0} x = 1$

$\map {P_1} x = x$

$\map {P_2} x = \dfrac 1 2 \paren {3 x^2 - 1}$

$\map {P_3} x = \dfrac 1 2 \paren {5 x^3 - 3 x}$

$\map {P_4} x = \dfrac 1 8 \paren {35 x^4 - 30 x^2 + 3}$