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lagder(c, m=1, scl=1, axis=0)

Returns the Laguerre 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 .

Notes

In general, the result of differentiating a Laguerre 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.

Parameters

c : array_like: Array of Laguerre series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.
m : int, optional: Number of derivatives taken, must be non-negative. (Default: 1)
scl : scalar, optional: 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 : int, optional: Axis over which the derivative is taken. (Default: 0).

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Returns

der : ndarray: Laguerre series of the derivative.

Differentiate a Laguerre series.

Examples

>>> from numpy.polynomial.laguerre import lagder
... lagder([ 1.,  1.,  1., -3.])
array([1.,  2.,  3.])

>>> lagder([ 1.,  0.,  0., -4.,  3.], m=2)
array([1.,  2.,  3.])

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

numpy.polynomial.laguerre.lagint

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