numpy.polynomial.hermite_e.hermefromroots — NumPy v1.15 Manual (original) (raw)
numpy.polynomial.hermite_e. hermefromroots(roots)[source]¶
Generate a HermiteE series with given roots.
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 * He_1(x) + ... + c_n * He_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). |
See also
polyfromroots, legfromroots, lagfromroots, hermfromroots, chebfromroots.
Examples
from numpy.polynomial.hermite_e import hermefromroots, hermeval coef = hermefromroots((-1, 0, 1)) hermeval((-1, 0, 1), coef) array([ 0., 0., 0.]) coef = hermefromroots((-1j, 1j)) hermeval((-1j, 1j), coef) array([ 0.+0.j, 0.+0.j])