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Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
Chebyshev's equation is the second order linear differential equation + = where p is a real (or complex) constant. The equation is named after Russian mathematician Pafnuty Chebyshev. The solutions can be obtained by power series:
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.
Many applications for Chebyshev nodes, such as the design of equally terminated passive Chebyshev filters, cannot use Chebyshev nodes directly, due to the lack of a root at 0. However, the Chebyshev nodes may be modified into a usable form by translating the roots down such that the lowest roots are moved to zero, thereby creating two roots at ...
Microsoft Math contains features that are designed to assist in solving mathematics, science, and tech-related problems, as well as to educate the user. The application features such tools as a graphing calculator and a unit converter. It also includes a triangle solver and an equation solver that provides step-by-step solutions to each problem.
In numerical analysis, the Clenshaw algorithm, also called Clenshaw summation, is a recursive method to evaluate a linear combination of Chebyshev polynomials. [1] [2] The method was published by Charles William Clenshaw in 1955. It is a generalization of Horner's method for evaluating a linear combination of monomials.
In numerical linear algebra, the Chebyshev iteration is an iterative method for determining the solutions of a system of linear equations. The method is named after Russian mathematician Pafnuty Chebyshev. Chebyshev iteration avoids the computation of inner products as is necessary for the other nonstationary methods. For some distributed ...
In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the ...
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