chaospy.expansion.legendre¶

chaospy.expansion.legendre(order, lower=- 1, upper=1, physicist=False, normed=False, retall=False)[source]¶

Examples:

>>> polynomials, norms = chaospy.expansion.legendre(3, retall=True)
>>> polynomials.round(5)
polynomial([1.0, q0, q0**2-0.33333, q0**3-0.6*q0])
>>> norms
array([1.        , 0.33333333, 0.08888889, 0.02285714])
>>> chaospy.expansion.legendre(3, physicist=True).round(3)
polynomial([1.0, 1.5*q0, 2.5*q0**2-0.556, 4.375*q0**3-1.672*q0])
>>> chaospy.expansion.legendre(3, lower=0, upper=1, normed=True).round(3)
polynomial([1.0, 3.464*q0-1.732, 13.416*q0**2-13.416*q0+2.236,
            52.915*q0**3-79.373*q0**2+31.749*q0-2.646])