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2019•Russian MathematicsRequires access

On Some Generalizations of Sum of Powers of Natural Numbers

Andrei K. Svinin, S. V. Svinina

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Abstract

In this paper we consider some generalizations of sums of powers of natural numbers. In particular, we study the class of sums whose generating function is a power of the generating function for the classical sums of powers. We also consider the so-called binomial sums and solve the problem of constructing polynomials which allow to calculate the values of the corresponding sums in certain cases.

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What this paper is about

In this paper we consider some generalizations of sums of powers of natural numbers. In particular, we study the class of sums whose generating function is a power of the generating function for the classical sums of powers. We also consider the so-called binomial sums and solve the problem of constructing polynomials which allow to calculate the values of the corresponding sums in certain cases.

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OpenAlex reports 3 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper we consider some generalizations of sums of powers of natural numbers. In particular, we study the class of sums whose generating function is a power of the generating function for the classical sums of powers. We also consider the so-called binomial sums and solve the problem of constructing polynomials which allow to calculate the values of the corresponding sums in certain cases.

Key concepts: Sums of powers, Mathematics, Natural number, Binomial coefficient, Class (philosophy), Binomial (polynomial), Generating function, Function (biology)

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