numpy.polynomial.legendre.legder

numpy.polynomial.legendre.legder(cs, m=1, scl=1)

Differentiate a Legendre series.

Returns the series cs differentiated m times. At each iteration the result is multiplied by scl (the scaling factor is for use in a linear change of variable). The argument cs is the sequence of coefficients from lowest order “term” to highest, e.g., [1,2,3] represents the series P_0 + 2*P_1 + 3*P_2.

Parameters :

cs : array_like

1-D array of Legendre series coefficients ordered from low to high.

m : int, optional

Number of derivatives taken, must be non-negative. (Default: 1)

scl : scalar, optional

Each differentiation is multiplied by scl. The end result is multiplication by scl**m. This is for use in a linear change of variable. (Default: 1)

Returns :

der : ndarray

Legendre series of the derivative.

See also

legint

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 “un-intuitive,” albeit correct; see Examples section below.

Examples

>>> from numpy.polynomial import legendre as L
>>> cs = (1,2,3,4)
>>> L.legder(cs)
array([  6.,   9.,  20.])
>>> L.legder(cs,3)
array([ 60.])
>>> L.legder(cs,scl=-1)
array([ -6.,  -9., -20.])
>>> L.legder(cs,2,-1)
array([  9.,  60.])

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