GENERALIZATION OF THE POWER SUM ARISING IN THE THEORY OF INTEGRABLE HIERARCHIES

摘要

We consider a class of multiple sums involving odd powers of natural numbers. Such sums appear while considering the continuous limit of the integrable hierarchy of evolution equations associated with the Itoh-Narita-Bogoyavlenskii lattice. We discuss the problem of constructing polynomials that allow us to calculate the values of the corresponding sums. Bibliography: 13 titles.