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numpy.polynomial.legendre.Legendre

# Legendre Module (`numpy.polynomial.legendre`)¶

New in version 1.6.0.

This module provides a number of objects (mostly functions) useful for dealing with Legendre series, including a `Legendre` class that encapsulates the usual arithmetic operations. (General information on how this module represents and works with such polynomials is in the docstring for its “parent” sub-package, `numpy.polynomial`).

## Legendre Class¶

 `Legendre`(coef[, domain, window]) A Legendre series class.

## Basics¶

 `legval`(x, c[, tensor]) Evaluate a Legendre series at points x. `legval2d`(x, y, c) Evaluate a 2-D Legendre series at points (x, y). `legval3d`(x, y, z, c) Evaluate a 3-D Legendre series at points (x, y, z). `leggrid2d`(x, y, c) Evaluate a 2-D Legendre series on the Cartesian product of x and y. `leggrid3d`(x, y, z, c) Evaluate a 3-D Legendre series on the Cartesian product of x, y, and z. `legroots`(c) Compute the roots of a Legendre series. `legfromroots`(roots) Generate a Legendre series with given roots.

## Fitting¶

 `legfit`(x, y, deg[, rcond, full, w]) Least squares fit of Legendre series to data. `legvander`(x, deg) Pseudo-Vandermonde matrix of given degree. `legvander2d`(x, y, deg) Pseudo-Vandermonde matrix of given degrees. `legvander3d`(x, y, z, deg) Pseudo-Vandermonde matrix of given degrees.

## Calculus¶

 `legder`(c[, m, scl, axis]) Differentiate a Legendre series. `legint`(c[, m, k, lbnd, scl, axis]) Integrate a Legendre series.

## Algebra¶

 `legadd`(c1, c2) Add one Legendre series to another. `legsub`(c1, c2) Subtract one Legendre series from another. `legmul`(c1, c2) Multiply one Legendre series by another. `legmulx`(c) Multiply a Legendre series by x. `legdiv`(c1, c2) Divide one Legendre series by another. `legpow`(c, pow[, maxpower]) Raise a Legendre series to a power.

 `leggauss`(deg) Gauss-Legendre quadrature. `legweight`(x) Weight function of the Legendre polynomials.
 `legcompanion`(c) Return the scaled companion matrix of c. `legdomain` `legzero` `legone` `legx` `legtrim`(c[, tol]) Remove “small” “trailing” coefficients from a polynomial. `legline`(off, scl) Legendre series whose graph is a straight line. `leg2poly`(c) Convert a Legendre series to a polynomial. `poly2leg`(pol) Convert a polynomial to a Legendre series.