numpy.polynomial.laguerre.lagfromroots

polynomial.laguerre.lagfromroots(roots)

Generate a Laguerre series with given roots.

The function returns the coefficients of the polynomial

\[p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n),\]

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

\[p(x) = c_0 + c_1 * L_1(x) + ... + c_n * L_n(x)\]

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

Parameters

rootsarray_like

Sequence containing the roots.

Returns

outndarray

1-D array of coefficients. If all roots are real then out is a real array, if some of the roots are complex, then out is complex even if all the coefficients in the result are real (see Examples below).

See also

numpy.polynomial.polynomial.polyfromroots

numpy.polynomial.legendre.legfromroots

numpy.polynomial.chebyshev.chebfromroots

numpy.polynomial.hermite.hermfromroots

numpy.polynomial.hermite_e.hermefromroots

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])

numpy.polynomial.laguerre.lagint numpy.polynomial.laguerre.lagroots