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.