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
 Returns
 Sndarray
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. ])