Generating functions of Bernstein polynomials: Fourier series expansion and applications
Authors
A. Karagenc
- Department of Mathematics, Faculty of Science and Arts, Gaziantep University, TR-27310 Gaziantep, Türkiye.
M. Acikgoz
- Department of Mathematics, Faculty of Science and Arts, Gaziantep University, TR-27310 Gaziantep, Türkiye.
S. Araci
- Department of Computer Engineering, Faculty of Engineering, Hasan Kalyoncu University, TR-27010 Gaziantep, Türkiye.
Abstract
In this paper, we introduce the Fourier series expansion of the generating
function for Bernstein polynomials. We also present series formulas for the
generating function of Bernoulli polynomials. Furthermore, we establish
novel formulae between these series and Euler polynomials as well as
Zeta-type functions. The exploration of these connections sheds light on the
intricate relationships among these fundamental mathematical constructs.
Through these discoveries, we deepen our understanding of the interplay
between various polynomial families and associated mathematical functions.
These findings contribute to the broader landscape of mathematical analysis
and offer insights into the rich structure underlying theory of special functions.
Share and Cite
ISRP Style
A. Karagenc, M. Acikgoz, S. Araci, Generating functions of Bernstein polynomials: Fourier series expansion and applications, Journal of Mathematics and Computer Science, 37 (2025), no. 4, 386--394
AMA Style
Karagenc A., Acikgoz M., Araci S., Generating functions of Bernstein polynomials: Fourier series expansion and applications. J Math Comput SCI-JM. (2025); 37(4):386--394
Chicago/Turabian Style
Karagenc, A., Acikgoz, M., Araci, S.. "Generating functions of Bernstein polynomials: Fourier series expansion and applications." Journal of Mathematics and Computer Science, 37, no. 4 (2025): 386--394
Keywords
- Fourier series
- generating function
- Bernstein polynomials
- Bernoulli polynomials
- Euler polynomials
- Zeta functions
MSC
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