scipy.special.eval_chebys

scipy.special.eval_chebys(n, x, out=None) = <ufunc 'eval_chebys'>

Evaluate Chebyshev polynomial of the second kind on [-2, 2] at a point.

These polynomials are defined as

\[S_n(x) = U_n(x/2)\]

where \(U_n\) is a Chebyshev polynomial of the second kind. See 22.5.13 in [AS] for details.

Parameters

narray_like

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

xarray_like

Points at which to evaluate the Chebyshev polynomial

outndarray, optional

Optional output array for the function values

Returns

Sscalar or ndarray

Values of the Chebyshev polynomial

See also

roots_chebys

roots and quadrature weights of Chebyshev polynomials of the second kind on [-2, 2]

chebys

Chebyshev polynomial object

eval_chebyu

evaluate Chebyshev polynomials of the second kind

References

AS

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

Examples

>>> import scipy.special as sc

They are a scaled version of the Chebyshev polynomials of the second kind.

>>> x = np.linspace(-2, 2, 6)
>>> sc.eval_chebys(3, x)
array([-4.   ,  0.672,  0.736, -0.736, -0.672,  4.   ])
>>> sc.eval_chebyu(3, x / 2)
array([-4.   ,  0.672,  0.736, -0.736, -0.672,  4.   ])