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Dergiler / 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
Sayfa
137–143
Yayın Tarihi
2019-07-29
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

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Amaç & Hipotez:We study on the sums of powers of consecutive integers and alternating sums of power of consecutive integers.
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Temel Bulgular & Veri:We study on the sums of powers of consecutive integers and alternating sums of power of consecutive integers.
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Sonuç & Katkı:We derive many identities and correlations including Bernoulli, Euler and Genocchi polynomials and numbers.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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Kaynakça (7)

  1. Acikgoz, M., Koca, I., Araci, S. The evaluation of the sums of more general series by Bernstein polynomials, Journal of Analysis and Number Theory, 4(1) (2016), 71-74.
  2. Araci, S., Acikgoz, M., Sen, E. Some new formulae for Genocchi numbers and polynomials involving Bernoulli and Euler polynomials, International Journal of Mathematics and Mathematical Sciences, Vol. 2014 (2014), Article ID 760613, 7 pages. doi:10.1155/2014/760613
  3. Cheon, G.-S. A note on the Bernoulli and Euler polynomials, Applied Mathematics Letters, 16(3) (2003), 365-368.
  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.