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pro vyhledávání: '"Acikgoz, Mehmet"'
Akademický článek
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Let n,k be the positive integers, and let S_{k}(n) be the sums of the k-th power of positive integers up to n. By means of that we consider the evaluation of the sum of more general series by Bernstein polynomials. Additionally we show the reality of
Externí odkaz:
http://arxiv.org/abs/1404.7400
Publikováno v:
Turkish J Analysis Number Theory 1 (2013) 1-3
In the present paper, we deal mainly with arithmetic properties of Legendre polynomials by using their orthogonality property. We show that Legendre polynomials are proportional with Bernoulli, Euler, Hermite and Bernstein polynomials.
Externí odkaz:
http://arxiv.org/abs/1312.7838
Publikováno v:
Feng Qi, Serkan Araci, and Mehmet Acikgoz, On an analogue of Euler polynomials and related to extended fermionic p-adic integrals on Z_p, Iranian Journal of Science and Technology, Transaction A: Science 41 (2017), no. 3, 613--618
In the paper, using the extended fermionic $p$-adic integral on $\mathbb{Z}_p$, the authors find some applications of the umbral calculus. From these applications, the authors derive some identities on the weighted Euler numbers and polynomials. In o
Externí odkaz:
http://arxiv.org/abs/1312.2040
Publikováno v:
Adv. Stud. Contemp. Math. 24 (2014), No. 2, pp. 227-240
The fundamental objective of this paper is to obtain some interesting properties for $\left(h,q\right)$-Genocchi numbers and polynomials by using the fermionic $p$-adic $q$-integral on $\mathbb{Z}_{p}$ and mentioned in the paper $q$-Bernstein polynom
Externí odkaz:
http://arxiv.org/abs/1312.0255
The main objective of this paper is to introduce the modified q-Genocchi polynomials and to define their generating function. In the paper, we show new relations, which are explicit formula, derivative formula, multiplication formula, and some others
Externí odkaz:
http://arxiv.org/abs/1311.5992
Publikováno v:
J. Nonlinear Sci. Appl. 9 (2016), 2697--2704
In the present paper, we obtain new interesting relations and identities of the Apostol-Bernoulli polynomials of higher order, which are derived using a Bernoulli polynomial basis. Finally, by utilizing our method, we also derive formulas for the con
Externí odkaz:
http://arxiv.org/abs/1311.4148
In this work, we consider not only a discontinuous boundary-value problem with retarded argument and four supplementary transmission conditions at the two points of discontinuities but also, eigenparameter-dependent boundary conditions and obtain asy
Externí odkaz:
http://arxiv.org/abs/1307.0365
Publikováno v:
Appl. Math. Inf. Sci. 9, No. 5, 2657-2662 (2015)
In the present paper, we investigate some interesting properties including several special polynomials arising from Caputo-fractional derivative. From our investigation, we derive a lot of interesting identities of several special polynomials.
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Externí odkaz:
http://arxiv.org/abs/1305.3220