Summary of Delsarte's "Nombre de Solutions des Equations Polynomiales sur un Corps Fini"

Properties of Chebyshev polynomials

Ordinary differential equations and boundary value problems arise in many aspects of mathematical physics. Chebyshev differential equation is one special case of the Sturm-Liouville boundary value problem. Generating function, recursive formula, orthogonality, and Parseval's identity are some important properties of Chebyshev polynomials. Compared with a Fourier series, an interpolation function using Chebyshev polynomials is more accurate in approximating polynomial functions. -------- Des équations différentielles ordinaires et des problèmes de valeurs limites se posent dans de nombreux aspe…