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

Year 2019, Volume: 2 Issue: 2, 137 - 143, 29.07.2019

Uğur Duran , Mehmet Acikgoz

https://doi.org/10.33773/jum.519968
Cited By: 1

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.

Keywords

Euler numbers and polynomials Bernoulli numbers and polynomials Genocchi numbers and polynomials power sums

References

  • 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.
  • 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
  • Cheon, G.-S. A note on the Bernoulli and Euler polynomials, Applied Mathematics Letters, 16(3) (2003), 365-368.
  • Coen, L. E. S. Sums of Powers and the Bernoulli Numbers, Master Thesis, Eastern Illinois University, 1996.
  • 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.
  • Kim, T. A note on the alternating sums of powers of consecutive integers, Proceedings of the Jangjeon Mathematical Society, 8(2) (2005), 175-178.
  • Shen, Y.-Y. A note on the sums of powers of consecutive integers, Tunghai Science, 5 (2005), 101-106.

Year 2019, Volume: 2 Issue: 2, 137 - 143, 29.07.2019

Uğur Duran , Mehmet Acikgoz

https://doi.org/10.33773/jum.519968
Cited By: 1

Abstract

References

  • 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.
  • 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
  • Cheon, G.-S. A note on the Bernoulli and Euler polynomials, Applied Mathematics Letters, 16(3) (2003), 365-368.
  • Coen, L. E. S. Sums of Powers and the Bernoulli Numbers, Master Thesis, Eastern Illinois University, 1996.
  • 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.
  • Kim, T. A note on the alternating sums of powers of consecutive integers, Proceedings of the Jangjeon Mathematical Society, 8(2) (2005), 175-178.
  • Shen, Y.-Y. A note on the sums of powers of consecutive integers, Tunghai Science, 5 (2005), 101-106.
There are 7 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Uğur Duran 0000-0002-5717-1199

Mehmet Acikgoz 0000-0003-1091-9697

Publication Date July 29, 2019
Submission Date January 31, 2019
Acceptance Date December 3, 2019
Published in Issue Year 2019 Volume: 2 Issue: 2

Cite

APA 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, 2(2), 137-143. https://doi.org/10.33773/jum.519968
AMA Duran U, Acikgoz M. SOME COMPUTATIONS BETWEEN SUMS OF POWERS OF CONSECUTIVE INTEGERS AND ALTERNATING SUMS OF POWERS OF CONSECUTIVE INTEGERS. JUM. July 2019;2(2):137-143. doi:10.33773/jum.519968
Chicago Duran, Uğur, and Mehmet Acikgoz. “SOME COMPUTATIONS BETWEEN SUMS OF POWERS OF CONSECUTIVE INTEGERS AND ALTERNATING SUMS OF POWERS OF CONSECUTIVE INTEGERS”. Journal of Universal Mathematics 2, no. 2 (July 2019): 137-43. https://doi.org/10.33773/jum.519968.
EndNote Duran U, Acikgoz M (July 1, 2019) SOME COMPUTATIONS BETWEEN SUMS OF POWERS OF CONSECUTIVE INTEGERS AND ALTERNATING SUMS OF POWERS OF CONSECUTIVE INTEGERS. Journal of Universal Mathematics 2 2 137–143.
IEEE U. Duran and M. Acikgoz, “SOME COMPUTATIONS BETWEEN SUMS OF POWERS OF CONSECUTIVE INTEGERS AND ALTERNATING SUMS OF POWERS OF CONSECUTIVE INTEGERS”, JUM, vol. 2, no. 2, pp. 137–143, 2019, doi: 10.33773/jum.519968.
ISNAD Duran, Uğur - Acikgoz, Mehmet. “SOME COMPUTATIONS BETWEEN SUMS OF POWERS OF CONSECUTIVE INTEGERS AND ALTERNATING SUMS OF POWERS OF CONSECUTIVE INTEGERS”. Journal of Universal Mathematics 2/2 (July 2019), 137-143. https://doi.org/10.33773/jum.519968.
JAMA Duran U, Acikgoz M. SOME COMPUTATIONS BETWEEN SUMS OF POWERS OF CONSECUTIVE INTEGERS AND ALTERNATING SUMS OF POWERS OF CONSECUTIVE INTEGERS. JUM. 2019;2:137–143.
MLA Duran, Uğur and Mehmet Acikgoz. “SOME COMPUTATIONS BETWEEN SUMS OF POWERS OF CONSECUTIVE INTEGERS AND ALTERNATING SUMS OF POWERS OF CONSECUTIVE INTEGERS”. Journal of Universal Mathematics, vol. 2, no. 2, 2019, pp. 137-43, doi:10.33773/jum.519968.
Vancouver Duran U, Acikgoz M. SOME COMPUTATIONS BETWEEN SUMS OF POWERS OF CONSECUTIVE INTEGERS AND ALTERNATING SUMS OF POWERS OF CONSECUTIVE INTEGERS. JUM. 2019;2(2):137-43.

Cited By

Euler polynomials and alternating sums of powers of integers
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