Article
The Evaluation of the Sums of More General Series by Bernstein Polynomials
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Abstract
Let $n,k$ be the positive integer, and let $S_k(n)$ be the sums of the $k$-th power of positive integers up to $n$: $S_k(n) = \sum_{l=1}^n l^k$. By means of which we consider the evaluation of the sum of more general series by Bernstein polynomials. In addition, we show reality of our idea with some examples.
Keywords
Bernoulli numbers and polynomials, Bernstein polynomials, Sums of powers of integers
Citation
Acikgoz, M., Koca, I., & Araci, S. (2016). The evaluation of the sums of more general series by bernstein polynomials. Journal of Analysis & Number Theory, 4(1), 71–74. https://doi.org/10.18576/jant/040110
M. Acikgoz, I. Koca and S. Araci, “The evaluation of the sums of more general series by bernstein polynomials,” Journal of Analysis & Number Theory, vol. 4, no. 1, pp. 71–74, 2016, doi: 10.18576/jant/040110.
Acikgoz M, Koca I, Araci S. The evaluation of the sums of more general series by bernstein polynomials. Journal of Analysis & Number Theory. 2016;4(1):71–74. doi:10.18576/jant/040110.
Acikgoz, M., Koca, I. and Araci, S. (2016), ‘The evaluation of the sums of more general series by bernstein polynomials’, Journal of Analysis & Number Theory, 4(1), pp. 71–74. Available at: https://doi.org/10.18576/jant/040110.
Acikgoz, Mehmet, et al. “The Evaluation of the Sums of More General Series by Bernstein Polynomials.” Journal of Analysis & Number Theory, vol. 4, no. 1, 2016, pp. 71–74. https://doi.org/10.18576/jant/040110.
Acikgoz, Mehmet, Ilknur Koca, and Serkan Araci. “The Evaluation of the Sums of More General Series by Bernstein Polynomials.” Journal of Analysis & Number Theory 4, no. 1 (2016): 71–74. https://doi.org/10.18576/jant/040110.
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Published by: Engineering Journals
