scipy.special.
sh_jacobi#
- scipy.special.sh_jacobi(n, p, q, monic=False)[source]#
- Shifted Jacobi polynomial. - Defined by \[G_n^{(p, q)}(x) = \binom{2n + p - 1}{n}^{-1}P_n^{(p - q, q - 1)}(2x - 1),\]- where \(P_n^{(\cdot, \cdot)}\) is the nth Jacobi polynomial. - Parameters:
- nint
- Degree of the polynomial. 
- pfloat
- Parameter, must have \(p > q - 1\). 
- qfloat
- Parameter, must be greater than 0. 
- monicbool, optional
- If True, scale the leading coefficient to be 1. Default is False. 
 
- Returns:
- Gorthopoly1d
- Shifted Jacobi polynomial. 
 
 - Notes - For fixed \(p, q\), the polynomials \(G_n^{(p, q)}\) are orthogonal over \([0, 1]\) with weight function \((1 - x)^{p - q}x^{q - 1}\).