arXiv subjects
Publications and source records attributed to Kwara Nantomah.
In this recreative piece of work, we present Gauss' calendar formula with some examples to demonstrate how it is applied. Then, based on it, we give a formula for determining dates of particular week days of a given month, and some examples are also given to demonstrate how it is applied. The key mathematical concept behind the formulas is modular arithmetic.
By using some tools of analysis, we establish some analytical properties such as monotonicity and inequalities involving the hyperbolic sine integral function. As applications of some of the established properties, we obtain some rational bounds for the hyperbolic tangent function.
In 1974, Gautschi proved an intriguing inequality involving the gamma function $Γ$. Precisely, he proved that, for $z>0$, the harmonic mean of $Γ(z)$ and $Γ(1/z)$ can never be less than 1. In 2017, Alzer and Jameson extended this result to the digamma function $ψ$ by proving that, for $z>0$, the harmonic mean of $ψ(z)$ and $ψ(1/z)$ can never be less than $-γ$ where $γ$ is the Euler-Mascheroni constant. In this paper, our goal is to extend the results to the trigamma function $ψ'$. We prove among other things that, for $z>0$, the harmonic mean of $ψ'(z)$ and $ψ'(1/z)$ can never be greater than $π^2/6$.
In this paper, we prove logarithmically complete monotonicity properties of certain ratios of the $k$-gamma function. As a consequence, we deduce some inequalities involving the $k$-gamma and $k$-trigamma functions.
In this paper, we study completete monotonicity properties of the function $f_{a,k}(x)=ψ^{(k)}(x+a) - ψ^{(k)}(x) - \frac{ak!}{x^{k+1}}$, where $a\in(0,1)$ and $k\in \mathbb{N}_0$. Specifically, we consider the cases for $k\in \{ 2n: n\in \mathbb{N}_0 \}$ and $k\in \{ 2n+1: n\in \mathbb{N}_0 \}$. Subsequently, we deduce some inequalities involving the polygamma functions.
In this study, we obtain some convexity, monotonicity and additivity properties as well as some inequalities involving the Nielsen's $β$-function which was introduced in 1906.
In this paper, the authors establish some inequalities involving the Psi and $k$-Gamma functions. The procedure utilizes some monotonicity properties of some functions associated with the Psi and $k$-Gamma functions.
In this paper, the authors establish some inequalities involving the $q$-extension of the classical Gamma function. These inequalities provide bounds for certain ratios of the $q$-extended Gamma function. The procedure makes use of geometric convexity and monotonicy properties of certain functions associated with the $q$-extended Gamma function.
This paper is inspired by the work of J. Sándor in 2006. In the paper, the authors establish some double inequalities involving the ratio $ \frac{Γ_{q}(x+1)}{ Γ_{q} \left( x+\frac{1}{2}\right)}$, where $Γ_{q}(x)$ is the $q$-deformation of the classical Gamma function denoted by $Γ(x)$. The method employed in presenting the results makes use of Jackson's $q$-integral representation of the $q$-deformed Gamma function. In addition, Hölder's inequality for the $q$-integral, as well as some basic analytical techniques involving the $q$-analogue of the psi function are used. As a consequence, $q$-analogues of the classical Wendel's asymptotic relation are obtained. At the end, sharpness of the inequalities established in this paper is investigated.
In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions involving the the generalized Gamma functions. At the end, we pose some open problems.
In this paper, we present and prove some generalizations of some inequalities for the $p$-Gamma, $q$-Gamma and $k$-Gamma functions. Our approach makes use of the series representations of the psi, $p$-psi, $q$-psi and $k$-psi functions.
Some inequalities for the ratios of generalized digamma functions are presented. The approache makes use of the series representations of the $(q,k)$-digamma and $(p,q)$-digamma functions.
In this paper, we present the (p; q)-analogues of some inequalities concerning the digamma function. Our results generalize some earlier results.