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

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.