sh_jacobi — SciPy v1.15.2 Manual (original) (raw)

scipy.special.

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