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