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 and eval_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.

scipy.special.eval_sh_chebyu scipy.special.roots_legendre