Svinin Andrei K
Published 2018-06-19Version 1
In this paper some generalizations of the sum of powers of natural numbers is considered. In particular, the class of sums whose generating function is the power of the generating function for the classical sums of powers is studying. The so-called binomial sums are also considered. The problem of constructing polynomials that allow to calculate the values of the corresponding sums in certain cases is solved.
On two problems of Carlitz and their generalizations
The generating function of the $σ_1$ function
Transcendence of generating functions whose coefficients are multiplicative
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