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As reported by Wikipedia, Chebyshev's equation is the second order linear differential equation $$(1-x^2) {d^2 y \over d x^2} - x {d y \over d x} + p^2 y = 0 $$ where $p$ is a real constant.

Has equation above physical meaning? That is, is it used to model some physical phenomena?

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Despite the similarity of Chebyshev's equation with Legendre's equation, it does not occur often in physical sciences or engineering, however, solutions of Chebyshev's equation are of importance in numerical analysis such as solution to partial differential equations, smoothing of data etc. While, on the other hand, its close associate Legendre's equation occurs quite often in areas such as electrodynamics and quantum mechanics, among others.

Main Source: Mathematical Methods for Physics and Engineering: A Comprehensive Guide - By K. F. Riley, M. P. Hobson, S. J. Bence

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Chebyshev's equation can be used to generate polynomials that could serve as mathematical model to approximate some observed physical phenomena.

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