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.