Fonctions for transformed Legendre polynomials, orthonormal on [0,1]:

$L_n(x) = \frac{\sqrt{4n^2-1}}{n}(2x-1)L_{n-1}(x)-\frac{(n-1)\sqrt{2n+1}}{n \sqrt{2n-3}} L_{n-2}(x),$

with $L_0(x)=1$ , $L_1(x)=\sqrt{3}(2x-1)$ and $L_2(x) = \sqrt{5}(6x^2-6x+1)$ . More...

Functions
def	legendre.legendre00 (x)
	Implements the transformed Legendre polynomials of degree 0 $L_0(x) = 1$ . More...

def	legendre.legendre01 (x)
	Implements the transformed Legendre polynomials of degree 1 $L_1(x)=\sqrt{3}(2x-1)$ . More...

def	legendre.legendre02 (x)
	Implements the transformed Legendre polynomials of degree 2 $L_2(x)=\sqrt{5}(6x^2-6x+1)$ . More...

def	legendre.legendre03 (x)
	Implements the transformed Legendre polynomials of degree 3 $L_3(x)=\sqrt{7}(20 x^3 30 x^2+12x-1)$ . More...

def	legendre.legendre04 (x)
	Implements the transformed Legendre polynomials of degree 4. More...

def	legendre.legendre05 (x)
	Implements the transformed Legendre polynomials of degree 5. More...

def	legendre.legendre06 (x)
	Implements the transformed Legendre polynomials of degree 6. More...

def	legendre.legendre07 (x)
	Implements the transformed Legendre polynomials of degree 7. More...

Detailed Description

Fonctions for transformed Legendre polynomials, orthonormal on [0,1]:

$L_n(x) = \frac{\sqrt{4n^2-1}}{n}(2x-1)L_{n-1}(x)-\frac{(n-1)\sqrt{2n+1}}{n \sqrt{2n-3}} L_{n-2}(x),$

with $L_0(x)=1$ , $L_1(x)=\sqrt{3}(2x-1)$ and $L_2(x) = \sqrt{5}(6x^2-6x+1)$ .

See [1].

Definition in file legendre.py.

Functions