scipy.special.eval_jacobi

scipy.special.eval_jacobi(n, alpha, beta, x, out=None) = <ufunc 'eval_jacobi'>

Evaluate Jacobi polynomial at a point.

The Jacobi polynomials can be defined via the Gauss hypergeometric function \({}_2F_1\) as

\[P_n^{(\alpha, \beta)}(x) = \frac{(\alpha + 1)_n}{\Gamma(n + 1)} {}_2F_1(-n, 1 + \alpha + \beta + n; \alpha + 1; (1 - z)/2)\]

where \((\cdot)_n\) is the Pochhammer symbol; see poch. When \(n\) is an integer the result is a polynomial of degree \(n\). See 22.5.42 in [AS] for details.

Parameters

narray_like

Degree of the polynomial. If not an integer the result is determined via the relation to the Gauss hypergeometric function.

alphaarray_like

Parameter

betaarray_like

Parameter

xarray_like

Points at which to evaluate the polynomial

outndarray, optional

Optional output array for the function values

Returns

Pscalar or ndarray

Values of the Jacobi polynomial

See also

roots_jacobi

roots and quadrature weights of Jacobi polynomials

jacobi

Jacobi polynomial object

hyp2f1

Gauss hypergeometric function

References

AS

Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.