... 3.12,forsufficiently large integer k,weobtain4.32yk,1x sin2kx sinh2kx O1k. 4.40 In similar way, we can seek eigenfunction yk,2x corresponding λk,2 in the formyk,2xy1x, ... ProblemsUsing the relations 3.3 and 3.12,forsufficiently large integer k,weobtain4.1yk,1x sin2kx− sinh2kx O1k. 4.10Similarly, since Uj1yυx, sk,1/ 0for ... 2, the asymptotic formulas3.2 are valid for k ≥ N.4. The Asymptotic Formulas for the EigenfunctionsNow, we obtain asymptotic formulas for eigenfunctions under the distinct conditions on...