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comment
Tschebycheff Polynome
T(n,x); Computes T_n(x)
Trek(n,x); a recursiv version (for test purposes)
Tpoly(n); Computes the Chebyshev polynomials T_n
endcomment
function T(n,x)
## T(n,x) computes T_n(x) the trigonometric way.
s=size(x,n);
y=x;
signum=-mod(n,2)*2+1;
loop 1 to s(2);
z=x{#};
if z>1;
w=(z+sqrt(z^2-1))^n{#};
y{#}=(w+1/w)/2;
else;
if z<-1;
w=(-z+sqrt(z^2-1))^n{#};
y{#}=signum{#}*(w+1/w)/2;
else;
y{#}=cos(n{#}*acos(z));
endif;
endif;
end;
return y;
endfunction
function Trek(n,x)
## Computes the Chebyshev polynomial via the recursion formula.
if (n==0); return ones(size(x)); endif;
if (n==1); return x; endif;
z=ones(size(x))_x;
loop 3 to n+1;
z=z_(2*x*z[#-1]-z[#-2]);
end;
return z[n+1];
endfunction
function Tpoly (n)
## Computes the coefficients of the n-th chebyshev polynomial
## recursively.
t0=[1]; t1=[0,1];
if (n==0); return t0; endif;
if (n==1); return t1; endif;
loop 2 to n
t=(0|2*t1[1:#])-(t0|[0,0]);
t0=t1; t1=t;
end;
return t;
endfunction
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