numpy.polynomial.hermite_e.hermeint(c, m=1, k=[], lbnd=0, scl=1, axis=0)
[source]
Integrate a Hermite_e series.
Returns the Hermite_e series coefficients c
integrated m
times from lbnd
along axis
. At each iteration the resulting series is multiplied by scl
and an integration constant, k
, is added. The scaling factor is for use in a linear change of variable. (“Buyer beware”: note that, depending on what one is doing, one may want scl
to be the reciprocal of what one might expect; for more information, see the Notes section below.) The argument c
is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the series 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: 


Returns: 

Raises: 

See also
Note that the result of each integration is multiplied by scl
. Why is this important to note? Say one is making a linear change of variable in an integral relative to x
. Then , so one will need to set scl
equal to  perhaps not what one would have first thought.
Also note that, in general, the result of integrating a Cseries needs to be “reprojected” onto the Cseries basis set. Thus, typically, the result of this function is “unintuitive,” albeit correct; see Examples section below.
>>> from numpy.polynomial.hermite_e import hermeint >>> hermeint([1, 2, 3]) # integrate once, value 0 at 0. array([1., 1., 1., 1.]) >>> hermeint([1, 2, 3], m=2) # integrate twice, value & deriv 0 at 0 array([0.25 , 1. , 0.5 , 0.33333333, 0.25 ]) # may vary >>> hermeint([1, 2, 3], k=1) # integrate once, value 1 at 0. array([2., 1., 1., 1.]) >>> hermeint([1, 2, 3], lbnd=1) # integrate once, value 0 at 1 array([1., 1., 1., 1.]) >>> hermeint([1, 2, 3], m=2, k=[1, 2], lbnd=1) array([ 1.83333333, 0. , 0.5 , 0.33333333, 0.25 ]) # may vary
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https://docs.scipy.org/doc/numpy1.17.0/reference/generated/numpy.polynomial.hermite_e.hermeint.html