SciPy

scipy.special.eval_chebyu

scipy.special.eval_chebyu(n, x, out=None) = <ufunc 'eval_chebyu'>

Evaluate Chebyshev polynomial of the second kind at a point.

The Chebyshev polynomials of the second kind can be defined via the Gauss hypergeometric function \({}_2F_1\) as

\[U_n(x) = (n + 1) {}_2F_1(-n, n + 2; 3/2; (1 - x)/2).\]

When \(n\) is an integer the result is a polynomial of degree \(n\).

Parameters:

n : array_like

Degree of the polynomial. If not an integer, the result is determined via the relation to the Gauss hypergeometric function.

x : array_like

Points at which to evaluate the Chebyshev polynomial

Returns:

U : ndarray

Values of the Chebyshev polynomial

See also

u_roots
roots and quadrature weights of Chebyshev polynomials of the second kind
chebyu
Chebyshev polynomial object
eval_chebyt
evaluate Chebyshev polynomials of the first kind
hyp2f1
Gauss hypergeometric function