`numpy.polynomial.legendre:legder`

source: build-install/usr/lib/python3.14/site-packages/numpy/polynomial/legendre.py :612

Signature

def legder ( c , m = 1 , scl = 1 , axis = 0 )

Summary

Differentiate a Legendre series.

Extended Summary

Returns the Legendre 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 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.
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: Legendre series of the derivative.

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)

✗

L.legder(c, 3)
L.legder(c, scl=-1)

✓

L.legder(c, 2,-1)

✗

Aliases

numpy.polynomial.Legendre._der
numpy.polynomial.legendre.legder