New in version 1.4.0.
Chebyshev Series (numpy.polynomial.chebyshev
)¶
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” subpackage, numpy.polynomial
).
Constants¶
Arithmetic¶

Add one Chebyshev series to another. 

Subtract one Chebyshev series from another. 

Multiply a Chebyshev series by x. 

Multiply one Chebyshev series by another. 

Divide one Chebyshev series by another. 

Raise a Chebyshev series to a power. 

Evaluate a Chebyshev series at points x. 

Evaluate a 2D Chebyshev series at points (x, y). 

Evaluate a 3D Chebyshev series at points (x, y, z). 

Evaluate a 2D Chebyshev series on the Cartesian product of x and y. 

Evaluate a 3D Chebyshev series on the Cartesian product of x, y, and z. 
Calculus¶

Differentiate a Chebyshev series. 

Integrate a Chebyshev series. 
Misc Functions¶

Generate a Chebyshev series with given roots. 

Compute the roots of a Chebyshev series. 

PseudoVandermonde matrix of given degree. 

PseudoVandermonde matrix of given degrees. 

PseudoVandermonde matrix of given degrees. 

GaussChebyshev quadrature. 

The weight function of the Chebyshev polynomials. 
Return the scaled companion matrix of c. 


Least squares fit of Chebyshev series to data. 

Chebyshev points of the first kind. 

Chebyshev points of the second kind. 

Remove “small” “trailing” coefficients from a polynomial. 

Chebyshev series whose graph is a straight line. 

Convert a Chebyshev series to a polynomial. 

Convert a polynomial to a Chebyshev series. 

Interpolate a function at the Chebyshev points of the first kind. 
See also¶
Notes¶
The implementations of multiplication, division, integration, and differentiation use the algebraic identities [1]:
where
These identities allow a Chebyshev series to be expressed as a finite, symmetric Laurent series. In this module, this sort of Laurent series is referred to as a “zseries.”
References¶
 1
A. T. Benjamin, et al., “Combinatorial Trigonometry with Chebyshev Polynomials,” Journal of Statistical Planning and Inference 14, 2008 (preprint: https://www.math.hmc.edu/~benjamin/papers/CombTrig.pdf, pg. 4)