Infinite Product Representation Of Solution Of Indefinite Sturm­Liouville Problem

In this paper, we investigate infinite product representation of the solution of a sturm-liouville equation with an indefinite weight function which has two zeros and/or singularities in a finite interval. first, by using of the asymptotic estimates provided in [w. eberhard, g. freiling, k. wilcken-stoeber, indefinite eigenvalue problems with several singular points and turning points, math. nachr. 229, 51-71 (2001)] for a special fundamental system of the solutions of sturm-liouville equation, we obtain the asymptotic behavior of it’s solutions and eigenvalues, then we obtain the infinite product representation of solution of the equation.