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// PG (220)
deff('[y]=f(x)','y=exp(x)')
// Chebyshev expansion coefficients for exp(x)
// j = 0
C0=2*(integrate('exp(cos(x))','x',0,3.14))/(3.14)
// j = 1
C1=2*(integrate('exp(cos(x))*cos(x)','x',0,3.14))/(3.14)
// j = 2
C2=2*(integrate('exp(cos(x))*cos(2*x)','x',0,3.14))/(3.14)
// j = 3
C3=2*(integrate('exp(cos(x))*cos(3*x)','x',0,3.14))/(3.14)
// j = 4
C4=2*(integrate('exp(cos(x))*cos(4*x)','x',0,3.14))/(3.14)
// j = 5
C5=2*(integrate('exp(cos(x))*cos(5*x)','x',0,3.14))/(3.14)
// we obtain
x=0:.01:%pi; // defining the range of x
c1=1.266+1.130*x;
c3=0.994571+0.997308*x+0.542991*x.^2+0.177347*x.^3;
norm(exp(x)-c1,'inf')
norm(exp(x)-c3,'inf')
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