Generate a Hermite series with given roots.
The function returns the coefficients of the polynomial\[p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n),\]
in Hermite form, where the r_n are the roots specified in
roots. If a zero has multiplicity n, then it must appear in
rootsn times. For instance, if 2 is a root of multiplicity three and 3 is a root of multiplicity 2, then
rootslooks something like [2, 2, 2, 3, 3]. The roots can appear in any order.
If the returned coefficients are c, then\[p(x) = c_0 + c_1 * H_1(x) + ... + c_n * H_n(x)\]
The coefficient of the last term is not generally 1 for monic polynomials in Hermite form.
Sequence containing the roots.
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).
>>> from numpy.polynomial.hermite import hermfromroots, hermval >>> coef = hermfromroots((-1, 0, 1)) >>> hermval((-1, 0, 1), coef) array([0., 0., 0.]) >>> coef = hermfromroots((-1j, 1j)) >>> hermval((-1j, 1j), coef) array([0.+0.j, 0.+0.j])