T_n(x)

Let's verify it for :math:`n = 3`:

>>> from scipy.special import binom
>>> from scipy.special import jacobi
>>> x = np.arange(-1.0, 1.0, 0.01)
>>> np.allclose(jacobi(3, -0.5, -0.5)(x),
...             1/64 * binom(6, 3) * chebyt(3)(x))
True

We can plot the Chebyshev polynomials :math:`T_n` for some values
of :math:`n`:

>>> x = np.arange(-1.5, 1.5, 0.01)
>>> fig, ax = plt.subplots()
>>> ax.set_ylim(-4.0, 4.0)
>>> ax.set_title(r'Chebyshev polynomials $T_n$')
>>> for n in np.arange(2,5):
...     ax.plot(x, chebyt(n)(x), label=rf'$T_n={n}$')
>>> plt.legend(loc='best')
>>> plt.show()

r