numpy.polynomial.hermite.hermder¶
- numpy.polynomial.hermite.hermder(c, m=1, scl=1, axis=0)[source]¶
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
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.])