Doklady Mathematics

, Volume 98, Issue 2, pp 486–489 | Cite as

Green’s Function of Ordinary Differential Operators and an Integral Representation of Sums of Certain Power Series

  • K. A. MirzoevEmail author
  • T. A. Safonova


The eigenvalues and eigenfunctions of certain operators generated by symmetric differential expressions with constant coefficients and self-adjoint boundary conditions in the space of Lebesgue squareintegrable functions on an interval are explicitly calculated, while the resolvents of these operators are integral operators with kernels for which the theorem on an eigenfunction expansion holds. In addition, each of these kernels is the Green’s function of a self-adjoint boundary value problem, and the procedure for its construction is well known. Thus, the Green’s functions of these problems can be expanded in series in terms of eigenfunctions. In this study, identities obtained by this method are used to calculate the sums of convergent number series and to represent the sums of certain power series in an intergral form.


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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia
  2. 2.Lomonosov Northern Arctic Federal UniversityArkhangelskRussia

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