scipy.special.eval_sh_chebyu¶

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

Evaluate shifted Chebyshev polynomial of the second kind at a point.

These polynomials are defined as

$U_n^*(x) = U_n(2x - 1)$

where $$U_n$$ is a Chebyshev polynomial of the first kind. See 22.5.15 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 shifted Chebyshev polynomial

Returns
Undarray

Values of the shifted Chebyshev polynomial

roots_sh_chebyu

roots and quadrature weights of shifted Chebychev polynomials of the second kind

sh_chebyu

shifted 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.

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