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

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