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_2while [[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
xand axis=1 is
- 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).
- der : ndarray
Hermite series of the derivative.
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.
>>> 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.])