DUAL RECURSIVE FORMULAS FOR THE SUMS OF POWERS OF INTEGERS
Keywords:
sums of powers of integers, symmetry property of the power sum polynomials, dual recursive formulasDOI:
https://doi.org/10.17654/0973563124012Abstract
In this note, we introduce the concept of a dual pair of recursive formulas for the sums of powers of integers
$$
S_k(n)=1^k+2^k+\cdots+n^k .
$$
Central to this concept is the symmetry property exhibited by the power sum polynomial $S_k(n)$. We illustrate the concept by some examples taken from the literature, and derive our own pair of dual recursive formulas for $S_k(n)$.
Received: September 16, 2024
Revised: October 16, 2024
Accepted: October 21, 2024
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