The Three Trace Formula Of Sturm-liouville Problem With Boundary Conditions

In this paper, the three different traces formula of eigenvalue problem conditions are researched. A(x),C(x),B(x)∈C2[0,π].First, we construct an entire function by use of the asymptotic estimations of solutions of initial value problem for Ly=λy.The zero set of the entire function coincide with the eigenvalue set of Ly=λy under corresponding boundary condition. By restorting to the integral identity:Using the residue method, we obtain trace formulas respectively for above three problems.