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This sum is called a Chebyshev series or a Chebyshev expansion. Since a Chebyshev series is related to a Fourier cosine series through a change of variables, all of the theorems, identities, etc. that apply to Fourier series have a Chebyshev counterpart. [16] These attributes include: The Chebyshev polynomials form a complete orthogonal system.
One can obtain polynomials very close to the optimal one by expanding the given function in terms of Chebyshev polynomials and then cutting off the expansion at the desired degree. This is similar to the Fourier analysis of the function, using the Chebyshev polynomials instead of the usual trigonometric functions.
The Chebyshev Lambda Linkage is used in vehicle suspension mechanisms, walking robots, and rover wheel mechanisms. In 2004, a study completed as a Master of Science Thesis at Izmir Institute of Technology introduced a new mechanism design by combining two symmetrical Lambda linkages to distribute the force evenly on to ground with providing the ...
In kinematics, Chebyshev's linkage is a four-bar linkage that converts rotational motion to approximate linear motion. It was invented by the 19th-century mathematician Pafnuty Chebyshev , who studied theoretical problems in kinematic mechanisms .
The Chebyshev nodes of the second kind, also called the Chebyshev extrema, are the extrema of the Chebyshev polynomials of the first kind, which are also the zeros of the Chebyshev polynomials of the second kind. Both of these sets of numbers are commonly referred to as Chebyshev nodes in literature. [1]
In numerical analysis Chebyshev–Gauss quadrature is an extension of Gaussian quadrature method for approximating the value of integrals of the following kind:
In mathematics, discrete Chebyshev polynomials, or Gram polynomials, are a type of discrete orthogonal polynomials used in approximation theory, introduced by Pafnuty Chebyshev [1] and rediscovered by Gram. [2] They were later found to be applicable to various algebraic properties of spin angular momentum.
The first Chebyshev function ϑ (x) or θ (x) is given by ϑ ( x ) = ∑ p ≤ x log p {\displaystyle \vartheta (x)=\sum _{p\leq x}\log p} where log {\displaystyle \log } denotes the natural logarithm , with the sum extending over all prime numbers p that are less than or equal to x .