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.
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.
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.
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. Temmuz 2019;2(2):137-143. doi:10.33773/jum.519968
Chicago
Duran, Uğur, ve Mehmet Acikgoz. “SOME COMPUTATIONS BETWEEN SUMS OF POWERS OF CONSECUTIVE INTEGERS AND ALTERNATING SUMS OF POWERS OF CONSECUTIVE INTEGERS”. Journal of Universal Mathematics 2, sy. 2 (Temmuz 2019): 137-43. https://doi.org/10.33773/jum.519968.
EndNote
Duran U, Acikgoz M (01 Temmuz 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 ve M. Acikgoz, “SOME COMPUTATIONS BETWEEN SUMS OF POWERS OF CONSECUTIVE INTEGERS AND ALTERNATING SUMS OF POWERS OF CONSECUTIVE INTEGERS”, JUM, c. 2, sy. 2, ss. 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 (Temmuz 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 ve Mehmet Acikgoz. “SOME COMPUTATIONS BETWEEN SUMS OF POWERS OF CONSECUTIVE INTEGERS AND ALTERNATING SUMS OF POWERS OF CONSECUTIVE INTEGERS”. Journal of Universal Mathematics, c. 2, sy. 2, 2019, ss. 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.