`numpy.polynomial.laguerre:lagfromroots`

source: /numpy/polynomial/laguerre.py :251

Signature

def lagfromroots ( roots )

Summary

Generate a Laguerre series with given roots.

Extended Summary

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

roots : array_like: Sequence containing the roots.

Returns

out : ndarray: 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).

Examples

from numpy.polynomial.laguerre import lagfromroots, lagval
coef = lagfromroots((-1, 0, 1))

✓

lagval((-1, 0, 1), coef)

✗

coef = lagfromroots((-1j, 1j))
lagval((-1j, 1j), coef)

✓

Aliases

numpy.polynomial.Laguerre._fromroots
numpy.polynomial.laguerre.lagfromroots