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.