24 citations · 33 across the 13 of their papers we have counts for
13 papers
On three classes of logarithmic integrals
Necdet Batır, Nandan Sai Dasireddy
In this paper, we evaluate the following families of definite integrals in closed form and we show that they are expressible only in terms of the dilogarithm function and the inver…
Logarithmic integrals with applications to BBP and Euler-type sums
Necdet Batir
For real numbers 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}\qu…
On some Binomial Coefficient Identities with Applications
Necdet Batir, Sezer Sorgunand Sevda Atpinar
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}\binomα{n-k}\binom{β+k…
Four types of variant Euler harmonic sums
Necdet Batir, Junesang Choi
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…
Parametric binomial sums involving harmonic numbers
Necdet Batir
We present explicit formulas for the following family of parametric binomial sums involving harmonic numbers for and . $$ \sum_{k=1}^{\infty}\frac{H_{k-1}t^k}{k…
An alternating proof of sharp inequalities related with Burnside's formula
Necdet Batir
We provide an alternating proof of sharp inequalities related with Burnside's formula for
Inequalities involving the gamma and digamma functions
Necdet Batir
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].…
Sharp inequalities related with Burnside's formula
Necdet Batir
We prove the following double inequality related with Burnside's formula for \begin{equation*} \sqrt{2π}\left(\frac{n+a_*}{e}\right)^{n+a_*}<n!<\sqrt{2π}\left(\frac{n+a^*}{e}\…
Combinatorial identities involving harmonic numbers
Necdet Batir
In this work we prove a new combinatorial identity and applying it we establish many finite harmonic sum identities. Among many others, we prove that \begin{equation*} \sum_{k=1}^{…
Inequalities for the inverses of the polygamma functions
Necdet Batir
We provide an elementary proof of the left side inequality and improve the right inequality in \bigg[\frac{n!}{x-(x^{-1/n}+α)^{-n}}\bigg]^{\frac{1}{n+1}}&<((-1)^{n-1}ψ^{(n)})^{-1}(…
Bounds for the gamma function
Necdet Batir
We improve the upper bound of the following inequalities for the gamma function due to H. Alzer and the author. \begin{equation*} \exp\left(-\frac{1}{2}ψ(x+1/3)\right)<\frac{Γ(…
On some combinatorial identities and harmonic sums
Necdet Batir
For any we first give new proofs for the following well known combinatorial identities \begin{equation*} S_n(m)=\sum\limits_{k=1}^n\binom{n}{k}\frac{(-1)^{k-1}}{…
On the series
Necdet Batir
In this paper we investigate the series . Obtaining some integral representations of them, we evaluated the sum of them explicitly…