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# Chebyshev Module (`numpy.polynomial.chebyshev`)¶

New in version 1.4.0.

This module provides a number of objects (mostly functions) useful for dealing with Chebyshev series, including a `Chebyshev` 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`).

## Chebyshev Class¶

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

## Basics¶

 `chebval`(x, c[, tensor]) Evaluate a Chebyshev series at points x. `chebval2d`(x, y, c) Evaluate a 2-D Chebyshev series at points (x, y). `chebval3d`(x, y, z, c) Evaluate a 3-D Chebyshev series at points (x, y, z). `chebgrid2d`(x, y, c) Evaluate a 2-D Chebyshev series on the Cartesian product of x and y. `chebgrid3d`(x, y, z, c) Evaluate a 3-D Chebyshev series on the Cartesian product of x, y, and z. Compute the roots of a Chebyshev series. `chebfromroots`(roots) Generate a Chebyshev series with given roots.

## Fitting¶

 `chebfit`(x, y, deg[, rcond, full, w]) Least squares fit of Chebyshev series to data. `chebvander`(x, deg) Pseudo-Vandermonde matrix of given degree. `chebvander2d`(x, y, deg) Pseudo-Vandermonde matrix of given degrees. `chebvander3d`(x, y, z, deg) Pseudo-Vandermonde matrix of given degrees.

## Calculus¶

 `chebder`(c[, m, scl, axis]) Differentiate a Chebyshev series. `chebint`(c[, m, k, lbnd, scl, axis]) Integrate a Chebyshev series.

## Algebra¶

 `chebadd`(c1, c2) Add one Chebyshev series to another. `chebsub`(c1, c2) Subtract one Chebyshev series from another. `chebmul`(c1, c2) Multiply one Chebyshev series by another. Multiply a Chebyshev series by x. `chebdiv`(c1, c2) Divide one Chebyshev series by another. `chebpow`(c, pow[, maxpower]) Raise a Chebyshev series to a power.

 `chebgauss`(deg) Gauss-Chebyshev quadrature. The weight function of the Chebyshev polynomials.

## Miscellaneous¶

 Return the scaled companion matrix of c. `chebdomain` `chebzero` `chebone` `chebx` `chebtrim`(c[, tol]) Remove “small” “trailing” coefficients from a polynomial. `chebline`(off, scl) Chebyshev series whose graph is a straight line. Convert a Chebyshev series to a polynomial. `poly2cheb`(pol) Convert a polynomial to a Chebyshev series.