# scipy.special.jacobi¶

scipy.special.jacobi(n, alpha, beta, monic=False)[source]

Jacobi polynomial.

Defined to be the solution of

$(1 - x^2)\frac{d^2}{dx^2}P_n^{(\alpha, \beta)} + (\beta - \alpha - (\alpha + \beta + 2)x) \frac{d}{dx}P_n^{(\alpha, \beta)} + n(n + \alpha + \beta + 1)P_n^{(\alpha, \beta)} = 0$

for $$\alpha, \beta > -1$$; $$P_n^{(\alpha, \beta)}$$ is a polynomial of degree $$n$$.

Parameters: n : int Degree of the polynomial. alpha : float Parameter, must be greater than -1. beta : float Parameter, must be greater than -1. monic : bool, optional If True, scale the leading coefficient to be 1. Default is False. P : orthopoly1d Jacobi polynomial.

Notes

For fixed $$\alpha, \beta$$, the polynomials $$P_n^{(\alpha, \beta)}$$ are orthogonal over $$[-1, 1]$$ with weight function $$(1 - x)^\alpha(1 + x)^\beta$$.

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