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Chebyshev polynomial

Chebyshev differential equation

{c}

The Chebyshev equation has self-adjoint form
$$
\left(\sqrt{1-x^2}\,T_n'\right)'
+\frac{n^2}{\sqrt{1-x^2}}T_n=0.
$$
For $U_n=T_n'$, differentiation gives
$$
\left((1-x^2)^{3/2}U_n'\right)'
+(n^2-1)\sqrt{1-x^2}\,U_n=0.
$$
The respective orthogonality weights are $(1-x^2)^{-1/2}$ and $(1-x^2)^{1/2}$.


Chebyshev derivative Sturm-Liouville pair

Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 2 / 3B / Solution

Chebyshev derivative Sturm-Liouville pair

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Chebyshev derivative Sturm-Liouville pair

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