# numpy.polynomial.legendre.legder¶

`numpy.polynomial.legendre.``legder`(c, m=1, scl=1, axis=0)[source]

Differentiate a Legendre series.

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). New in version 1.7.0. 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)
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.])
```

#### Previous topic

numpy.polynomial.legendre.legvander3d

#### Next topic

numpy.polynomial.legendre.legint