numpy.polynomial.legendre.legfromroots(roots)
[source]
Generate a Legendre series with given roots.
The function returns the coefficients of the polynomial
in Legendre 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 Legendre form.
Parameters: |
roots : array_like Sequence containing the roots. |
---|---|
Returns: |
out : ndarray 1-D array of coefficients. If all roots are real then |
See also
polyfromroots
, chebfromroots
, lagfromroots
, hermfromroots
, hermefromroots.
>>> 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) >>> 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])
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https://docs.scipy.org/doc/numpy-1.12.0/reference/generated/numpy.polynomial.legendre.legfromroots.html