numpy.polynomial.laguerre.lagint()

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.

Notes

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.

Examples

>>> 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.        ])