Zobrazeno 1 - 10
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pro vyhledávání: '"Batır, Necdet"'
Autor:
Batir, Necdet
For real numbers $p,q>1$ we consider the following family of integrals: \begin{equation*} \int_{0}^{1}\frac{(x^{q-2}+1)\log\left(x^{mq}+1\right)}{x^q+1}{\rm d}x \quad \mbox{and}\quad \int_{0}^{1}\frac{(x^{pt-2}+1)\log\left(x^t+1\right)}{x^{pt}+1}{\rm
Externí odkaz:
http://arxiv.org/abs/2302.06640
We present a different proof of the following identity due to Munarini, which generalizes a curious binomial identity of Simons. \begin{align*} \sum_{k=0}^{n}\binom{\alpha}{n-k}\binom{\beta+k}{k}x^k &=\sum_{k=0}^{n}(-1)^{n+k}\binom{\beta-\alpha+n}{n-
Externí odkaz:
http://arxiv.org/abs/2301.09587
Autor:
Batir, Necdet, Choi, Junesang
We aim to investigate the four types of variant Euler harmonic sums. Also, as corollaries, we provide particular examples of our core findings, some of whose further instances are evaluated in terms of basic and well-known functions as well as certai
Externí odkaz:
http://arxiv.org/abs/2301.06317
Autor:
Batır, Necdet, Choi, Junesang
Publikováno v:
In Journal of Mathematical Analysis and Applications 15 October 2024 538(2)
Autor:
Batır, Necdet1 (AUTHOR) nbatir@hotmail.com, Choi, Junesang2 (AUTHOR) junesang@dongguk.ac.kr
Publikováno v:
Mathematics (2227-7390). Aug2024, Vol. 12 Issue 16, p2450. 20p.
Autor:
Choi, Junesang1 (AUTHOR) junesang@dongguk.ac.kr, Batır, Necdet2 (AUTHOR) nbatir@hotmail.com
Publikováno v:
Symmetry (20738994). Jul2024, Vol. 16 Issue 7, p932. 32p.
Autor:
Batir, Necdet
We present explicit formulas for the following family of parametric binomial sums involving harmonic numbers for $p=0,1,2$ and $|t|\leq1$. $$ \sum_{k=1}^{\infty}\frac{H_{k-1}t^k}{k^p\binom{n+k}{k}}\quad \mbox{and}\quad \sum_{k=1}^{\infty}\frac{t^k}{k
Externí odkaz:
http://arxiv.org/abs/2105.03927
Akademický článek
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Autor:
Batir, Necdet
We provide an alternating proof of sharp inequalities related with Burnside's formula for $n!$
Comment: 4 pages
Comment: 4 pages
Externí odkaz:
http://arxiv.org/abs/1911.02824
Autor:
Batir, Necdet
We improve the upper bounds of the following inequalities proved in [H. Alzer and N. Batir, Monotonicity properties of the gamma function, Appl. Math. Letters, 20(2007), 778-781]. \begin{equation*} exp\left(-\frac{1}{2}\psi\left(x+\frac{1}{3}\right)\
Externí odkaz:
http://arxiv.org/abs/1812.05343