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SciPy

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scipy.special.jacobi

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

Jacobi polynomial.

Defined to be the solution of

(1x2)d2dx2P(α,β)n+(βα(α+β+2)x)ddxP(α,β)n+n(n+α+β+1)P(α,β)n=0

for α,β>1; P(α,β)n 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.

Returns:

P : orthopoly1d

Jacobi polynomial.

Notes

For fixed α,β, the polynomials P(α,β)n are orthogonal over [1,1] with weight function (1x)α(1+x)β.

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