chaospy.expansion.jacobi

chaospy.expansion.jacobi(order, alpha, beta, lower=- 1, upper=1, physicist=False, normed=False, retall=False)

Jacobi polynomial expansion.

Examples:

>>> polynomials, norms = chaospy.expansion.jacobi(4, 0.5, 0.5, retall=True)
>>> polynomials
polynomial([1.0, q0, q0**2-0.5, q0**3-0.75*q0, q0**4-q0**2+0.125])
>>> norms
array([1.       , 0.5      , 0.125    , 0.03125  , 0.0078125])
>>> chaospy.expansion.jacobi(3, 0.5, 0.5,  physicist=True).round(4)
polynomial([1.0, 1.5*q0, 2.5*q0**2-0.8333, 4.375*q0**3-2.1146*q0])
>>> chaospy.expansion.jacobi(3, 1.5, 0.5, normed=True)
polynomial([1.0, 2.0*q0, 4.0*q0**2-1.0, 8.0*q0**3-4.0*q0])