CL_chebyshevPoly

Description

• Computes Chebyshev polynomials of first or second kind.

  The polynomials are defined as follows:

  P0(x) = 1 (degree 0)

  P1(x) = kind * x, with kind = 1 or 2 (degree 1)

  Pn(x) = 2 * x * Pn-1(x) - Pn-2(x), for n >= 2

  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)

kind:

(optional) 1 for first kind, 2 for second kind. Default is 1 (1x1)

p:

Chebyshev 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

See also

• CL_chebyshevEval

Examples

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