scipy.special.eval_sh_jacobi¶
-
scipy.special.
eval_sh_jacobi
(n, p, q, x, out=None) = <ufunc 'eval_sh_jacobi'>¶ Evaluate shifted Jacobi polynomial at a point.
Defined by
\[G_n^{(p, q)}(x) = \binom{2n + p - 1}{n}^{-1} P_n^{(p - q, q - 1)}(2x - 1),\]where \(P_n^{(\cdot, \cdot)}\) is the n-th Jacobi polynomial. See 22.5.2 in [AS] for details.
- Parameters
- nint
Degree of the polynomial. If not an integer, the result is determined via the relation to
binom
andeval_jacobi
.- pfloat
Parameter
- qfloat
Parameter
- Returns
- Gndarray
Values of the shifted Jacobi polynomial.
See also
roots_sh_jacobi
roots and quadrature weights of shifted Jacobi polynomials
sh_jacobi
shifted Jacobi polynomial object
eval_jacobi
evaluate Jacobi polynomials
References
- AS
Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.