numpy.polynomial.laguerre.lagint(c, m=1, k=[], lbnd=0, scl=1, axis=0)
[source]
Integrate a Laguerre series.
Returns the Laguerre 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 L_0 + 2*L_1 + 3*L_2
while [[1,2],[1,2]] represents 1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y) + 2*L_0(x)*L_1(y) + 2*L_1(x)*L_1(y)
if axis=0 is x
and axis=1 is y
.
Parameters: |
c : array_like Array of Laguerre series coefficients. If m : int, optional Order of integration, must be positive. (Default: 1) k : {[], list, scalar}, optional Integration constant(s). The value of the first integral at lbnd : scalar, optional The lower bound of the integral. (Default: 0) scl : scalar, optional Following each integration the result is multiplied by axis : int, optional Axis over which the integral is taken. (Default: 0). New in version 1.7.0. |
---|---|
Returns: |
S : ndarray Laguerre series coefficients of the integral. |
Raises: |
ValueError If |
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 .. math::dx = du/a
, 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 C-series needs to be “reprojected” onto the C-series basis set. Thus, typically, the result of this function is “unintuitive,” albeit correct; see Examples section below.
>>> from numpy.polynomial.laguerre import lagint >>> lagint([1,2,3]) array([ 1., 1., 1., -3.]) >>> lagint([1,2,3], m=2) array([ 1., 0., 0., -4., 3.]) >>> lagint([1,2,3], k=1) array([ 2., 1., 1., -3.]) >>> lagint([1,2,3], lbnd=-1) array([ 11.5, 1. , 1. , -3. ]) >>> lagint([1,2], m=2, k=[1,2], lbnd=-1) array([ 11.16666667, -5. , -3. , 2. ])
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https://docs.scipy.org/doc/numpy-1.12.0/reference/generated/numpy.polynomial.laguerre.lagint.html