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# numpy.polynomial.chebyshev.chebfromroots

`numpy.polynomial.chebyshev.``chebfromroots`(roots)

  Generate a Chebyshev series with given roots.

  The function returns the coefficients of the polynomial

  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

  The coefficient of the last term is not generally 1 for monic polynomials in Chebyshev 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`, `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+0.j,  0.5+0.j])

### Navigation

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- NumPy v1.7 Manual (DRAFT) »
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- Chebyshev Module (`numpy.polynomial.chebyshev`) »