CL_legendrePoly

Description

• Computes Legendre polynomials.

  Legendre polynomials are defined as follows:

  P0(x) = 1 (degree 0)

  P1(x) = x (degree 1)

  (k+1) * Pk+1(x) = (2*k+1)*Pk(x) - k * Pk-1(x) (for k >= 1)

  The function returns the polynomials of degree n. p(k) is the polynomial of degree n(k).

  The function also optionally returns the first and second derivatives of the polynomials.

Parameters

n:

(integer) Degrees of the polynomials in [0,100] (PxQ)

p:

Legendre polynomials (same size as n)

pdot:

First derivative of the polynomials (same size as p)

p2dot:

Second derivative of the polynomials (same size as p)

Authors

• CNES - DCT/SB

Examples

// Generate Legendre polynomials (degree 0 to 5) and plot them n = 0:5; p = CL_legendrePoly(n); t = linspace(-1,1,100); scf(); plot(t, horner(p',t)); CL_g_legend(gca(), "degree: " + string(n));