Series in root elements of the differential sheaf of tenth order with five-fold roots of the characteristic equation

From the point of view of widely known regular spectral tasks the problem under consideration has two essential singularities. Firstly, the five-fold rate of each of the two roots of the constitutive secular equation of the tenth order. Secondly, boundary conditions at the ends of the main interval fall into the type of decomposing conditions, only one of which set on the right and other nine on the left end. Irregularity of such conditions is well-known in classical boundary value problems. The spectrum of our problem is cleanly imaginary own values equidistant from each other. One own function and four functions added to it correspond to each own value. The article presents the construction of the sheaf resolvent (the Green function), as a meromorphic function of parameter $\lambda$. The basic theorem proves that the complete deduction by the parameter from the resolvent, attached to the ninefold differentiable function (becoming a zero at ends 0,1 together with all derivatives), equals this function. The indicated deduction, as is generally known, presents the row of Fourier on the root functions of the initial problem.