Generate a Chebyshev series with given roots.
The function returns the coefficients of the polynomial\[p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n),\]
in Chebyshev 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\[p(x) = c_0 + c_1 * T_1(x) + ... + c_n * T_n(x)\]
The coefficient of the last term is not generally 1 for monic polynomials in Chebyshev 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).
>>> import numpy.polynomial.chebyshev as C >>> C.chebfromroots((-1,0,1)) # x^3 - x relative to the standard basis array([ 0. , -0.25, 0. , 0.25]) >>> j = complex(0,1) >>> C.chebfromroots((-j,j)) # x^2 + 1 relative to the standard basis array([1.5+0.j, 0. +0.j, 0.5+0.j])