numpy.polynomial.laguerre.lagfromroots()

Generate a Laguerre series with given roots.

The function returns the coefficients of the polynomial

in Laguerre form, where the r_n are the roots specified in roots. If a zero has multiplicity n, then it must appear in roots n times. For instance, if 2 is a root of multiplicity three and 3 is a root of multiplicity 2, then roots looks something like [2, 2, 2, 3, 3]. The roots can appear in any order.

If the returned coefficients are c, then

The coefficient of the last term is not generally 1 for monic polynomials in Laguerre form.

Examples

>>> from numpy.polynomial.laguerre import lagfromroots, lagval
>>> coef = lagfromroots((-1, 0, 1))
>>> lagval((-1, 0, 1), coef)
array([ 0.,  0.,  0.])
>>> coef = lagfromroots((-1j, 1j))
>>> lagval((-1j, 1j), coef)
array([ 0.+0.j,  0.+0.j])