numpy.polynomial.hermite_e.hermeder

numpy.polynomial.hermite_e.hermeder(c, m=1, scl=1, axis=0)

Differentiate a Hermite_e series.

Returns the series coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl (the scaling factor is for use in a linear change of variable). The argument c is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the series 1*He_0 + 2*He_1 + 3*He_2 while [[1,2],[1,2]] represents 1*He_0(x)*He_0(y) + 1*He_1(x)*He_0(y) + 2*He_0(x)*He_1(y) + 2*He_1(x)*He_1(y) if axis=0 is x and axis=1 is y.

Parameters:

c : array_like

Array of Hermite_e series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.

m : int, optional

Number of derivatives taken, must be non-negative. (Default: 1)

scl : scalar, optional

Each differentiation is multiplied by scl. The end result is multiplication by scl**m. This is for use in a linear change of variable. (Default: 1)

axis : int, optional

Axis over which the derivative is taken. (Default: 0).

New in version 1.7.0.

Returns:

der : ndarray

Hermite series of the derivative.

See also

hermeint

Notes

In general, the result of differentiating a Hermite series does not resemble the same operation on a power series. Thus the result of this function may be “unintuitive,” albeit correct; see Examples section below.

Examples

>>> from numpy.polynomial.hermite_e import hermeder
>>> hermeder([ 1.,  1.,  1.,  1.])
array([1.,  2.,  3.])
>>> hermeder([-0.25,  1.,  1./2.,  1./3.,  1./4 ], m=2)
array([1.,  2.,  3.])