Recreating chebychev coefficient from an article

[dan_smith]

Hello i need to recreate these chebychev coefficents given the initial value of X_0=1.853 as shown in the photo bellow.
i have tried to follow the iterrative algorithm shown in the photo bellow.
please help me understand where did i go wrong?

thanks

 

[mfb]

please help me understand where did i go wrong?

What exactly went wrong?

 

[dan_smith]

What exactly went wrong?

if x_0=1.853 then
T_0=1
T_1=1.853
T_2=2*1.853*1.853-1
its not the same numbers that they get in the article

Thanks

 

[mfb]

What you calculate are not coefficients of polynomials, these numbers are the values of the polynomial functions at this value of x.

I don't understand where their numbers come from, but I also don't understand where they are used afterwards. I found the context here, page 19 ("206").

I also don't understand the value of x they got - WolframAlpha disagrees (using 180 instead of pi doesn't work either, but I guess the 180 comes from working in degrees).

 

[dan_smith]

Hello, Yes this is the article from which the example came from.
you are correct regarding the wolfram alfa calculation.assuming that their numbers are wrong
i tried to use matlabs commands for
g=chebyshevT([1 ,2, 3 ,4] , x) %first kind
[ x, 2*x^2 - 1, 4*x^3 - 3*x, 8*x^4 - 8*x^2 + 1]

g=chebyshevU([1 ,2, 3 ,4],x) %second kind
[ 2*x, 4*x^2 - 1, 8*x^3 - 4*x, 16*x^4 - 12*x^2 + 1]

what coefficients should i take for this step?

Thanks