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Journals / Journal of Universal Mathematics / 2019 / Cilt: 2 Sayı: 2

SOME COMPUTATIONS BETWEEN SUMS OF POWERS OF CONSECUTIVE INTEGERS AND ALTERNATING SUMS OF POWERS OF CONSECUTIVE INTEGERS

Uğur Duran(ISKENDERUN TECHNICAL UNIVERSITY)0000-0002-5717-1199
Mehmet Acikgoz(GAZİANTEP ÜNİVERSİTESİ)0000-0003-1091-9697
Pages
137–143
Publication Date
2019-07-29
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We derive many identities and correlations including Bernoulli, Euler and Genocchi polynomials and numbers.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We study on the sums of powers of consecutive integers and alternating sums of power of consecutive integers.
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Key Findings & Data:We study on the sums of powers of consecutive integers and alternating sums of power of consecutive integers.
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Conclusion & Impact:We derive many identities and correlations including Bernoulli, Euler and Genocchi polynomials and numbers.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Euler numbers and polynomials · Bernoulli numbers and polynomials · Genocchi numbers and polynomials

Abstract

We study on the sums of powers of consecutive integers and alternating sums of power of consecutive integers. We derive many identities and correlations including Bernoulli, Euler and Genocchi polynomials and numbers.

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Cite This Article

Duran, U., Acikgoz, M. (2019). SOME COMPUTATIONS BETWEEN SUMS OF POWERS OF CONSECUTIVE INTEGERS AND ALTERNATING SUMS OF POWERS OF CONSECUTIVE INTEGERS. Journal of Universal Mathematics, Cilt: 2 Sayı: 2, 137–143. https://doi.org/10.33773/jum.519968

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References (7)

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  4. Coen, L. E. S. Sums of Powers and the Bernoulli Numbers, Master Thesis, Eastern Illinois University, 1996.
  5. E.-Mikkawy, M., Atlan, F. Derivation of identities involving some special polynomials and numbers via generating functions with applications, Applied Mathematics and Computation, 220 (2013), 518-535.
  6. Kim, T. A note on the alternating sums of powers of consecutive integers, Proceedings of the Jangjeon Mathematical Society, 8(2) (2005), 175-178.
  7. Shen, Y.-Y. A note on the sums of powers of consecutive integers, Tunghai Science, 5 (2005), 101-106.