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Chebyshev's Differential Equation and Orthogonality of Chebyshev Polynomials
Автор: Mike, the Mathematician
Загружено: 2024-09-04
Просмотров: 533
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We use the definition of the Chebyshev polynomials (of the first kind, which are found here • Chebyshev Polynomials ) to find a second order differential equation for which these polynomials are a solution. We use the differential equation and to prove that two Chebyshev polynomials of different orders are orthogonal with respect to the measure dx/(sqrt(1-x^2)). This proves that the family of Chebyshev polynomials are an example of orthogonal polynomials.
#mikethemathematician, #mikedabkowski, #profdabkowski
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