Regularized traces of boundary problems in case of multiple roots of characteristic polynomial

The boundary problem on a segment for differential equation of $n$ order with coefficients polynomially depending on spectral parameter $\lambda$ is considered. In the general case of multiple roots of Tamarkin's characteristic polynomial the regularized traces, i.e. the sums $\sum\limits_k[\lambda_k^m-A_m(k)]$, $m\in\mathbb{N}$, are calculated, where $\lambda_k$ are eigenvalues of the problem, and $A_m(k)$ are totally defined numbers, ensuring the convergence of series.