scipy.special.sh_chebyu¶
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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 \((x - x^2)^{1/2}\).