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

Yıl 2019, Cilt: 2 Sayı: 2, 137 - 143, 29.07.2019

Uğur Duran Mehmet Acikgoz

https://doi.org/10.33773/jum.519968

Cited By: 1

Öz

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.

Anahtar Kelimeler

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

Kaynakça

• 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.