`numpy.polynomial.legendre:legfromroots`

source: build-install/usr/lib/python3.14/site-packages/numpy/polynomial/legendre.py :267

Signature

def legfromroots ( roots )

Summary

Generate a Legendre 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 Legendre 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 Legendre 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

import numpy.polynomial.legendre as L
L.legfromroots((-1,0,1)) # x^3 - x relative to the standard basis
j = complex(0,1)

✓

L.legfromroots((-j,j)) # x^2 + 1 relative to the standard basis

✗

Aliases

numpy.polynomial.Legendre._fromroots
numpy.polynomial.legendre.legfromroots