reapress null reapress3042-30903042-3090 reapress https://doi.org/10.22105/kmisj.v3i1.120 Research Article Chebyshev polynomials, Orthogonal polynomials, Pearson equation, Second-order differen tial equations, Sturm–Liouville theory, Spectral methods, Orthogonality, Approximation theory. On a Derivation of the Classical Differential Equation for Chebyshev Polynomials of the First KindOn a Derivation of the Classical Differential Equation for Chebyshev Polynomials of the First Kind Aliyev Jeyhun Department of General Mathematics, Nakhchivan State University, Nakhchivan, Azerbaijan. 03 2026 09 03 2026 3 1 © 2026 reapress 2026

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 On a Derivation of the Classical Differential Equation for Chebyshev Polynomials of the First Kind

In this study, the derivation of the second-order differential equation for first-order Chebyshev polynomials is revisited using orthogonality theory and the Pearson equation approach. By employing the Pearson-type relation associated with the Chebyshev weight function, the relationship between the weight function and the corresponding differential operator is systematically analyzed. This approach leads directly to the classical second-order differential equation satisfied by Chebyshev polynomials and reveals the Sturm–Liouville structure of the associated operator. The interplay between orthogonal polynomial systems and second-order differential equations is emphasized, highlighting the analytical structure underlying these polynomials. In particular, the Pearson equation framework provides an alternative and systematic derivation of the differential equation governing the Chebyshev polynomial system.

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