scipy.special.
sh_chebyu#
- scipy.special.sh_chebyu(n, monic=False)[source]#
- Shifted Chebyshev polynomial of the second kind. - Defined as \(U^*_n(x) = U_n(2x - 1)\) for \(U_n\) the nth Chebyshev polynomial of the second kind. - Parameters:
- nint
- Degree of the polynomial. 
- monicbool, optional
- If True, scale the leading coefficient to be 1. Default is False. 
 
- Returns:
- Uorthopoly1d
- Shifted Chebyshev polynomial of the second kind. 
 
 - Notes - The polynomials \(U^*_n\) are orthogonal over \([0, 1]\) with weight function \((x - x^2)^{1/2}\).