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We establish some new Tur\'an's type inequalities for orthogonal polynomials defined by a three-term recurrence with monotonic coefficients. As a corollary we deduce asymptotic bounds on the extreme zeros of orthogonal polynomials with…

Classical Analysis and ODEs · Mathematics 2011-01-18 Ilia Krasikov

We use Turan type inequalities to give new non-asymptotic bounds on the extreme zeros of orthogonal polynomials in terms of the coefficients of their three term recurrence. Most of our results deal with symmetric polynomials satisfying the…

Classical Analysis and ODEs · Mathematics 2025-10-20 Ilia Krasikov

This paper deals with both the higher order Tur\'an inequalities and the Laguerre inequalities for quasi-polynomial-like functions -- that are expressions of the form $f(n)=c_l(n)n^l+\cdots+c_d(n)n^d+o(n^d)$, where $d,l\in\mathbb{N}$ and…

Combinatorics · Mathematics 2023-10-24 Krystian Gajdzica

We show that the normalised ultraspherical polynomials, $G_n^{(\lambda)}(x)=C_n^{(\lambda)}(x)/C_n^{(\lambda)}(1)$, satisfy the following stronger version of Tur\'{a}n inequality, $$|x|^\theta \left(G_n^{(\lambda)}(x)\right)^2…

Classical Analysis and ODEs · Mathematics 2023-12-05 Ilia Krasikov

Let $g$ and $h$ be real-valued arithmetic functions, positive and normalized. Specific choices within the following general scheme of recursively defined polynomials \begin{equation*} P_n^{g,h}(x):= \frac{x}{h(n)} \sum_{k=1}^{n} g(k) \,…

Classical Analysis and ODEs · Mathematics 2022-04-05 Bernhard Heim , Markus Neuhauser , Robert Troeger

In this paper, our aim is to show some mean value inequalities for the Fox-Wright functions, such as Tur\'an--type inequalities, Lazarevi\'c and Wilker--type inequalities. As applications we derive some new type inequalities for…

Classical Analysis and ODEs · Mathematics 2017-08-23 Khaled Mehrez , Sergei M. Sitnik

Heim, Neuhauser, and Tr\"oger recently established some inequalities for MacMahon's plane partition function $\mathrm{PL}(n)$ that generalize known results for Euler's partition function $p(n)$. They also conjectured that $\mathrm{PL}(n)$…

Number Theory · Mathematics 2022-09-13 Ken Ono , Sudhir Pujahari , Larry Rolen

In this paper, we establish some inequalities for rational functions with prescribed poles having s-fold zeros at origin and also show that it implies some inequalities for polynomials and their polar derivatives.

Complex Variables · Mathematics 2025-02-24 Preeti Gupta

In this paper, some monotonicity and concavity results of several functions involving the psi and polygamma functions are proved, and then some known inequalities are extended and generalized.

Classical Analysis and ODEs · Mathematics 2010-08-03 Feng Qi , Bai-Ni Guo

In this paper we prove monotonicity of some ratios of $q$--Kummer confluent hypergeometric and $q$--hypergeometric functions. The results are also closely connected with Tur\'an type inequalities. In order to obtain main results we apply…

Classical Analysis and ODEs · Mathematics 2016-09-20 Khaled Mehrez , Sergei M. Sitnik

In this article we derive some polynomial inequalities for Mertens functions.

Number Theory · Mathematics 2019-02-11 R. Balasubramanian , S. Ponnusamy , K. -J. Wirths

In this paper we give some sharper refinements and generalizations of inequalities related to Shafer's inequality for the arctangent function, stated in Theorems 1, 2 and 4 in [1], by C. Mortici and H.M. Srivastava.

Classical Analysis and ODEs · Mathematics 2019-10-15 Branko Malesevic , Marija Rasajski , Tatjana Lutovac

In this paper, we not only give the extensions of the results given in [7] by Gill et al. for log-convex functions, but also obtain some new Hadamard type inequalities for log-convex, m-convex and (alpha,m)-convex functions.

Functional Analysis · Mathematics 2011-04-01 Erhan Set , M. Emin Ozdemir , Sever S. Dragomir

We present some completely monotonic functions involving the$q$-polygamma functions, our result generalizes some known results.

Classical Analysis and ODEs · Mathematics 2016-01-22 Peng Gao

We establish some monotonicity results and functional inequalities for modified Lommel functions of the first kind. In particular, we obtain new Tur\'{a}n type inequalities and bounds for ratios of modified Lommel functions of the first…

Classical Analysis and ODEs · Mathematics 2021-10-13 Robert E. Gaunt

In this paper first we survey the Tur\'an type inequalities and related problems for the Bessel functions of the first kind. Then we extend the known higher order Tur\'an type inequalities for Bessel functions of the first kind to real…

Classical Analysis and ODEs · Mathematics 2014-01-22 Árpád Baricz , Tibor K. Pogány

Complete monotonicity, Laguerre and Tur\'an type inequalities are established for the so-called Kr\"atzel function $Z_{\rho}^{\nu},$ defined by $$Z_{\rho}^{\nu}(u)=\int_0^{\infty}t^{\nu-1}e^{-t^{\rho}-\frac{u}{t}}\dt,$$ where $u>0$ and…

Classical Analysis and ODEs · Mathematics 2012-01-10 Árpád Baricz , Dragana Jankov , Tibor K. Pogány

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…

Classical Analysis and ODEs · Mathematics 2015-06-25 Kwara Nantomah

Motivated by some applications in applied mathematics, biology, chemistry, physics and engineering sciences, new tight Tur\'an type inequalities for modified Bessel functions of the first and second kind are deduced. These inequalities…

Classical Analysis and ODEs · Mathematics 2017-07-14 Árpád Baricz

In this paper our aim is to prove some monotonicity and convexity results for the modified Struve function of the second kind by using its integral representation. Moreover, as consequences of these results, we present some functional…

Classical Analysis and ODEs · Mathematics 2015-01-28 Árpád Baricz , Tibor K. Pogány