Generalization of the Power Sum Arising in the Theory of Integrable Hierarchies

详细

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.