chebyshev with sinus parameter as an input

Hello, is there a way to get an expression for P_n(sin (theta)) a chebyshev polynomial with sinus theta as an input parameter?

Thanks

Answer 1

[John D'Errico]

What have you tried? If nothing, then why not?

Easy enough to build a Chebychev polynomial, using the standard recursion relations. Wikipedia will surely give them, and I know that sufficient information can be found in Abramowitz and Stegun, because I wrote tools based on that long ago. My copy of Abramowitz and Stegun is so well used that I put tabs in it at a few useful pages. (A useful text.) Then you just make it into a function of theta, as you wish. So just create a function handle.

Probably easier yet is to download the chebfun toolbox, which will probably make it easy to solve that problem. So 2 simple lines of code.

p3 = chebpoly(3);
pfun = @(theta) p3(sin(theta));

pfun(.5)
ans =
     -0.99749

Or, if you wanted it for a general value of n, not fixed in advance as I did, then just write a function m-file.

[fima v]

Hello, i am trying to recreate this article example i tried functions like chebychefT but i cant get this specific numbers. what do you think they were using? Thanks