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numpy.polynomial.legendre.legfromroots¶

`numpy.polynomial.legendre.``legfromroots`(roots)[source]

Generate a Legendre series with given 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 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 * L_1(x) + ... + c_n * L_n(x)

The coefficient of the last term is not generally 1 for monic polynomials in Legendre form.

Parameters: roots : array_like Sequence containing the roots. 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).

`polyfromroots`, `chebfromroots`, `lagfromroots`, `hermfromroots`, `hermefromroots.`
```>>> import numpy.polynomial.legendre as L