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 \(n\). See 22.5.48 in [AS] for details.

Parameters

narray_like

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

xarray_like

Points at which to evaluate the Chebyshev polynomial

outndarray, optional

Optional output array for the function values

Returns

Uscalar or 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

References

AS

Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.