array of the integral. Raises ------ ValueError If ``m < 0``, ``len(k) > m``, ``np.ndim(lbnd) != 0``, or ``np.ndim(scl) != 0``. See Also -------- legder Notes ----- Note that the result of each integration is *multiplied* by `scl`. Why is this important to note? Say one is making a linear change of variable :math:`u = ax + b` in an integral relative to `x`. Then :math:`dx = du/a`, so one will need to set `scl` equal to :math:`1/a` - perhaps not what one would have first thought. Also note that, in general, the result of integrating a C-series needs to be "reprojected" onto the C-series basis set. Thus, typically, the result of this function is "unintuitive," albeit correct; see Examples section below. Examples -------- >>> from numpy.polynomial import legendre as L >>> c = (1,2,3) >>> L.legint(c) array([ 0.33333333, 0.4 , 0.66666667, 0.6 ]) # may vary >>> L.legint(c, 3) array([ 1.66666667e-02, -1.78571429e-02, 4.76190476e-02, # may vary -1.73472348e-18, 1.90476190e-02, 9.52380952e-03]) >>> L.legint(c, k=3) array([ 3.33333333, 0.4 , 0.66666667, 0.6 ]) # may vary >>> L.legint(c, lbnd=-2) array([ 7.33333333, 0.4 , 0.66666667, 0.6 ]) # may vary >>> L.legint(c, scl=2) array([ 0.66666667, 0.8 , 1.33333333, 1.2 ]) # may vary r