Sums of powers via backward finite differences and Newton's formula
Sums of powers via backward finite differences and Newton's formula
Abstract We obtain formulas for sums of powers via Newton’s interpolation formula based on backward finite differences of powers.In addition, we note that backward differences are closely related to Eulerian numbers, and Stirling numbers of the second kind.Thus, we express formulas for sums of powers in terms of Eulerian numbers, and Stirling numbers of the second kind. 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) Metadata DOI: https://doi.org/10.5281/zenodo.18118011 HTML: https://kolosovpetro.github.io/sums-of-powers-backward-differences/ MSC2010: 05A19, 05A10, 11B83, 03C40. Keywords: Sums of powers, Newton's interpolation formula, Finite differences, Binomial coefficients, Faulhaber's formula,Bernoulli numbers, Bernoulli polynomials, Interpolation, Combinatorics, Central factorial numbers, OEIS, Stirling numbers,Eulerian numbers, Worpitzky identity.
Sums of powers, Finite differences, Central factorial numbers, Bernoulli polynomials, Worpitzky identity, Interpolation, Stirling numbers, Faulhaber's formula, Combinatorics, Binomial coefficients, Newton's interpolation formula, Eulerian numbers, Bernoulli numbers, OEIS
Sums of powers, Finite differences, Central factorial numbers, Bernoulli polynomials, Worpitzky identity, Interpolation, Stirling numbers, Faulhaber's formula, Combinatorics, Binomial coefficients, Newton's interpolation formula, Eulerian numbers, Bernoulli numbers, OEIS
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