Quick and Easy Chebyshev T function

[Bobingstern]

Chebyshev polynomials of the first kind $T_n(x)$ can be implemented super easily using their trigonometric definition and as a result can be extended to complex values of n and x.
For values of
$|x|\leq 1$
$T_n(x)=\cos(n\arccos(x))$
and for
$|x| \geq 1$
$T_n(x)=\frac{1}{2}((x-\sqrt{x^2-1})^n+(x+\sqrt{x^2-1})^n)$

This is ridiculously easy to implement in math.js. The function name could be ChebyshevT just like that of Wolfram Mathematica

[Amanpatel2002-g]

May I know what the problem in it then.

[josdejong]

@Bobingstern is your proposal to implement a new function chebyshevT? That would be nice. Are there related functions that we should implement then too?