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scipy.special.jacobi¶
- scipy.special.jacobi(n, alpha, beta, monic=False)[source]¶
Jacobi polynomial.
Defined to be the solution of
(1−x2)d2dx2P(α,β)n+(β−α−(α+β+2)x)ddxP(α,β)n+n(n+α+β+1)P(α,β)n=0for 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 (1−x)α(1+x)β.