Newton's interpolation formula and sums of powers

Zenodo (CERN European Organization for Nuclear Research) 2026 Preprint Open access

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Authors: Petro Kolosov
DOI: 10.5281/zenodo.18159899
Cited by: 0

Abstract

Abstract In this manuscript we derive formulas for multifold sums of powers by utilizing Newton's interpolation formula. Furthermore, we provide formulas for multifold sums of powers in terms of Stirling numbers of the second kind and Eulerian numbers. Related works Newton's interpolation formula and sums of powers (2025) Sums of powers via central finite differences and Newton's formula (2025) Sums of powers via backward finite differences and Newton's formula (2026) OEIS https://oeis.org/A131689 - Triangle of numbers T(n,k) = k!*Stirling2(n,k) read by rows, T(n, k) for 0

Fields of Study & Subjects

Advanced Mathematical Identities Advanced Combinatorial Mathematics Mathematical Inequalities and Applications

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
6 January 2026
Language
EN
Document type
Preprint