`numpy.polynomial.hermite_e:hermefromroots`

source: /numpy/polynomial/hermite_e.py :256

Signature

def hermefromroots ( roots )

Summary

Generate a HermiteE 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 HermiteE 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} * H e_{1} (x) + ... + c_{n} * H e_{n} (x)

The coefficient of the last term is not generally 1 for monic polynomials in HermiteE 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.hermite_e import hermefromroots, hermeval
coef = hermefromroots((-1, 0, 1))
hermeval((-1, 0, 1), coef)
coef = hermefromroots((-1j, 1j))
hermeval((-1j, 1j), coef)

✓

Aliases

numpy.polynomial.HermiteE._fromroots
numpy.polynomial.hermite_e.hermefromroots