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
- Returns
- Pndarray
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.