The T(n, x) function computes the nth Chebyshev polynomial of the first kind evaluated at x.

These polynomials are orthogonal on the interval ($\mathrm{-1},1$) with respect to the weight function $w\left(x\right)=\frac{1}{\sqrt{-x^2+1}}$. They satisfy:

Chebyshev polynomials of the first kind satisfy the following recurrence relation:

$\mathrm{with}\left(\mathrm{orthopoly}\right)\:$

$T\left(2\,x\right)$

$2x^2-1$

$T\left(3\,x\right)$

$4x^3-3x$

$T\left(50\,\frac{1}{3}\right)$

$\frac{203160711589551869872313}{717897987691852588770249}$