legfromroots(roots)
The function returns the coefficients of the polynomial
$$p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n),$$in Legendre form, where the :None:None:`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 :None:None:`c`, then
The coefficient of the last term is not generally 1 for monic polynomials in Legendre form.
Sequence containing the roots.
1-D array of coefficients. If all roots are real then :None:None:`out` is a real array, if some of the roots are complex, then :None:None:`out` is complex even if all the coefficients in the result are real (see Examples below).
Generate a Legendre series with given roots.
>>> import numpy.polynomial.legendre as L
... L.legfromroots((-1,0,1)) # x^3 - x relative to the standard basis array([ 0. , -0.4, 0. , 0.4])
>>> j = complex(0,1)See :
... L.legfromroots((-j,j)) # x^2 + 1 relative to the standard basis array([ 1.33333333+0.j, 0.00000000+0.j, 0.66666667+0.j]) # may vary
The following pages refer to to this document either explicitly or contain code examples using this.
numpy.polynomial.hermite.hermfromroots
numpy.polynomial.polynomial.polyfromroots
numpy.polynomial.chebyshev.chebfromroots
numpy.polynomial.hermite_e.hermefromroots
numpy.polynomial.laguerre.lagfromroots
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