`numpy.polynomial.chebyshev`

source: build-install/usr/lib/python3.14/site-packages/numpy/polynomial/chebyshev.py :0

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Summary

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Additional content

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" sub-package, numpy.polynomial).

Classes

.. autosummary:: 
    :toctree:generated/
    Chebyshev

Constants

.. autosummary:: 
    :toctree:generated/
    chebdomain
    chebzero
    chebone
    chebx

Arithmetic

.. autosummary:: 
    :toctree:generated/
    chebadd
    chebsub
    chebmulx
    chebmul
    chebdiv
    chebpow
    chebval
    chebval2d
    chebval3d
    chebgrid2d
    chebgrid3d

Calculus

.. autosummary:: 
    :toctree:generated/
    chebder
    chebint

Misc Functions

.. autosummary:: 
    :toctree:generated/
    chebfromroots
    chebroots
    chebvander
    chebvander2d
    chebvander3d
    chebgauss
    chebweight
    chebcompanion
    chebfit
    chebpts1
    chebpts2
    chebtrim
    chebline
    cheb2poly
    poly2cheb
    chebinterpolate

Notes

The implementations of multiplication, division, integration, and differentiation use the algebraic identities ^[1]:

T_{n} (x) = \frac{z ^{n} + z ^{- n}}{2} z \frac{d x}{d z} = \frac{z - z ^{- 1}}{2} .

where

x = \frac{z + z ^{- 1}}{2} .

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 "z-series."

References

[1]

Polynomials," Journal of Statistical Planning and Inference 14, 2008 (https://web.archive.org/web/20080221202153/https://www.math.hmc.edu/~benjamin/papers/CombTrig.pdf, pg. 4)

Aliases

numpy.polynomial.chebyshev