numpy.polynomial.legendre.legder
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numpy.polynomial.legendre.legder(c, m=1, scl=1, axis=0)
[source] -
Differentiate a Legendre series.
Returns the Legendre series coefficients
c
differentiatedm
times alongaxis
. At each iteration the result is multiplied byscl
(the scaling factor is for use in a linear change of variable). The argumentc
is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the series1*L_0 + 2*L_1 + 3*L_2
while [[1,2],[1,2]] represents1*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 isx
and axis=1 isy
.- Parameters
-
-
carray_like
-
Array of Legendre series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.
-
mint, optional
-
Number of derivatives taken, must be non-negative. (Default: 1)
-
sclscalar, optional
-
Each differentiation is multiplied by
scl
. The end result is multiplication byscl**m
. This is for use in a linear change of variable. (Default: 1) -
axisint, optional
-
Axis over which the derivative is taken. (Default: 0).
New in version 1.7.0.
-
- Returns
-
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derndarray
-
Legendre series of the derivative.
-
See also
Notes
In general, the result of differentiating a Legendre 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 import legendre as L >>> c = (1,2,3,4) >>> L.legder(c) array([ 6., 9., 20.]) >>> L.legder(c, 3) array([60.]) >>> L.legder(c, scl=-1) array([ -6., -9., -20.]) >>> L.legder(c, 2,-1) array([ 9., 60.])
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https://numpy.org/doc/1.19/reference/generated/numpy.polynomial.legendre.legder.html