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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
As a special case, alternating sums of powers of integers are also considered, and some new polynomial expressions are given.
📌 3 Key Takeaways
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Objective & Hypothesis:The possible polynomial expressions for sums of powers of integers multiplied by an exponential term are investigated.
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Key Findings & Data:We explicitly give factorization of these polynomials in terms of the roots of Apostol-Bernoulli polynomials.
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Conclusion & Impact:As a special case, alternating sums of powers of integers are also considered, and some new polynomial expressions are given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Sum of powers of integers · Faulhaber's theorem · alternating sums of power
Abstract
The possible polynomial expressions for sums of powers of integers multiplied by an exponential term are investigated. We explicitly give factorization of these polynomials in terms of the roots of Apostol-Bernoulli polynomials. As a special case, alternating sums of powers of integers are also considered, and some new polynomial expressions are given.
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Cite This Article
ERDOĞAN, A. (2019). A note on polynomial expressions for sums of power of integers multiplied by exponential terms. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 1, 199–206. https://ajindex.com/articles/214996