orthax.laguerre.lagder

orthax.laguerre.lagder(c, m=1, scl=1, axis=0)Source

Differentiate a Laguerre series.

Returns the Laguerre series coefficients c differentiated m times along axis. At each iteration the result is multiplied by 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.

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 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).

Returns:

der (ndarray) – Laguerre series of the derivative.

See also

lagint

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.

Examples

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