scipy.special.sh_jacobi

scipy.special.sh_jacobi(n, p, q, monic=False)

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