New in version 1.6.0.

# Legendre Series (`numpy.polynomial.legendre`)#

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`).

## Classes#

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

## Constants#

 `legdomain` An array object represents a multidimensional, homogeneous array of fixed-size items. `legzero` An array object represents a multidimensional, homogeneous array of fixed-size items. `legone` An array object represents a multidimensional, homogeneous array of fixed-size items. `legx` An array object represents a multidimensional, homogeneous array of fixed-size items.

## Arithmetic#

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

## Calculus#

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

## Misc Functions#

 `legfromroots`(roots) Generate a Legendre series with given roots. Compute the roots of a Legendre series. `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. `leggauss`(deg) Gauss-Legendre quadrature. Weight function of the Legendre polynomials. Return the scaled companion matrix of c. `legfit`(x, y, deg[, rcond, full, w]) Least squares fit of Legendre series to data. `legtrim`(c[, tol]) Remove "small" "trailing" coefficients from a polynomial. `legline`(off, scl) Legendre series whose graph is a straight line. Convert a Legendre series to a polynomial. `poly2leg`(pol) Convert a polynomial to a Legendre series.