legder(c, m=1, scl=1, axis=0)
Returns the Legendre series coefficients c differentiated m times along :None:None:`axis`. At each iteration the result is multiplied by :None:None:`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*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
.
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.
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.
Number of derivatives taken, must be non-negative. (Default: 1)
Each differentiation is multiplied by :None:None:`scl`. The end result is multiplication by scl**m
. This is for use in a linear change of variable. (Default: 1)
Axis over which the derivative is taken. (Default: 0).
Legendre series of the derivative.
Differentiate a Legendre series.
>>> 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.])See :
The following pages refer to to this document either explicitly or contain code examples using this.
numpy.polynomial.legendre.legint
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