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 \((1 - x)^{p - q}x^{q - 1}\).