# 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.

## Miscellaneous¶

 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.