Published January 1, 2026
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Sums of powers via backward finite differences and Newton's formula
Authors/Creators
Description
Abstract
We develop formula for sums of powers using Newton's interpolation formula in terms of backward finite differences of powers.
Metadata
DOI: https://doi.org/10.5281/zenodo.18118011
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.
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SumsOfPowersViaBackwardFiniteDifferencesAndNewtonFormula.pdf
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Additional details
Software
- Repository URL
- https://github.com/kolosovpetro/SumsOfPowersViaBackwardFiniteDifferencesAndNewtonFormula
- Development Status
- Active
References
- Knuth, D. E. (1993). Johann Faulhaber and sums of powers. Mathematics of Computation, 61(203), 277–294. https://arxiv.org/abs/math/9207222
- Sloane, N. J. A., et al. (2003). The on-line encyclopedia of integer sequences. https://oeis.org/
- Steffensen, J. F. (1927). Interpolation. Williams & Wilkins. https://www.amazon.com/-/de/Interpolation-Second-Dover-Books-Mathematics-ebook/dp/B00GHQVON8