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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

roots_chebyu

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