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Orthogonal Polynomials >> Orthogonal Polynomials > Chebyshev > chebyshev_eval

chebyshev_eval

Evaluate Chebyshev polynomial

Calling Sequence

y=chebyshev_eval(x,n)

Parameters

x :

a matrix of doubles

n :

a 1-by-1 matrix of doubles, integer value, n>=0.

y :

a matrix of doubles, the function value

Description

Evaluates a Chebyshev polynomial of degree n at point x.

The first Chebyshev polynomials are

The remaining Chebyshev polynomials satisfy the recurrence:

for n=1,2,...

Examples

x=linspace(-1,1,100);
y0=chebyshev_eval(x,0);
y1=chebyshev_eval(x,1);
y2=chebyshev_eval(x,2);
y3=chebyshev_eval(x,3);
h=scf();
plot(x,y0,"r-")
plot(x,y1,"g-")
plot(x,y2,"b-")
plot(x,y3,"c:")
xtitle("Chebyshev Polynomials","x","T(x)")
legend(["n=0","n=1","n=2","n=3"]);
h.children.data_bounds(1:2,2)=[-1.1;1.1];
h.children.children(4).children.thickness=3;
h.children.children(5).children.thickness=2;
h.children.children(5).children.line_style=5;

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