scipy.special.

sh_jacobi#

scipy.special.sh_jacobi(n, p, q, monic=False)[source]#

Shifted Jacobi polynomial.

Defined by

Gn(p,q)(x)=(2n+p1n)1Pn(pq,q1)(2x1),

where Pn(,) is the nth Jacobi polynomial.

Parameters:
nint

Degree of the polynomial.

pfloat

Parameter, must have p>q1.

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 Gn(p,q) are orthogonal over [0,1] with weight function (1x)pqxq1.