Over the openning problems of singuler differantial operators in spektral theory

This study contains three parts.At the first part, some definitions and theories, often used on the theories of differancial operators are told.At the second part, Legendre Functions are studied, the relation with some functions, openning formules and asymptotic formules are dwelled on.At the third part, classical Fourier Integral is studied, Fourier-Bessel serial opennings, Fourier-Hankel Integral openning are told, orthogonal Hermite Functions are touched and Cebysev-Laguerre polinom opennings are studied.Key words: Sturm-Liouville Problem, eigenvalue, eigenvalue function, Legendre functions, Bessel functions