# 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. chebroots(c) 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. chebmulx(c) 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. chebweight(x) The weight function of the Chebyshev polynomials.

## Miscellaneous¶

 chebcompanion(c) 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. cheb2poly(c) Convert a Chebyshev series to a polynomial. poly2cheb(pol) Convert a polynomial to a Chebyshev series.