numpy.polynomial.hermite.hermder

numpy.polynomial.hermite.hermder(c, m=1, scl=1, axis=0)

Differentiate a Hermite series.

Returns the Hermite 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*H_0 + 2*H_1 + 3*H_2 while [[1,2],[1,2]] represents 1*H_0(x)*H_0(y) + 1*H_1(x)*H_0(y) + 2*H_0(x)*H_1(y) + 2*H_1(x)*H_1(y) if axis=0 is x and axis=1 is y.

Parameters:

c : array_like

Array of Hermite 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

hermint

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 import hermder
>>> hermder([ 1. ,  0.5,  0.5,  0.5])
array([ 1.,  2.,  3.])
>>> hermder([-0.5,  1./2.,  1./8.,  1./12.,  1./16.], m=2)
array([ 1.,  2.,  3.])