# 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 U : ndarray Values of the Chebyshev polynomial

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

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