Abstract
UDC 517.9 This paper is devoted to determine the asymptotic formulae for eigenfunctions of the periodic and semi-periodic Hill's equation when the potential is symmetric single well. The obtained results for eigenvalues by H. Coşkun and the others (2019) are used. With this estimates on the eigenfunctions, Green's functions related to the Hill's equation are obtained. The method is based on the work of C. T. Fulton (1977) to derive Green's functions in an asymptotical manner. We need the derivatives of the solutions in this method. Therefore, the asymptotic approximations for the derivatives of the eigenfunctions are also calculated with different types of restrictions on the potential.
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