numpy.polynomial.chebyshev.chebfromroots   polynomial.chebyshev.chebfromroots(roots)[source]
 
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 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  \[p(x) = c_0 + c_1 * T_1(x) + ... + c_n * T_n(x)\] The coefficient of the last term is not generally 1 for monic polynomials in Chebyshev form.  Parameters 
 
rootsarray_like


Sequence containing the roots.    Returns 
 
outndarray


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  numpy.polynomial.polynomial.polyfromroots
numpy.polynomial.legendre.legfromroots
numpy.polynomial.laguerre.lagfromroots
numpy.polynomial.hermite.hermfromroots
numpy.polynomial.hermite_e.hermefromroots
  Examples >>> 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])