Related papers: On integrals involving quotients of hyperbolic fun…
This paper deals with some inequalities for trigonometric and hyperbolic functions such as the Jordan inequality and its generalizations. In particular, lower and upper bounds for functions such as (sin x)/x and x/(sinh x) are proved.
Investigation of the generalized trigonometric and hyperbolic functions containing two parameters has been a very active research area over the last decade. We believe, however, that their monotonicity and convexity properties with respect…
The table of Gradshteyn and Rhyzik contains some trigonometric integrals that can be expressed in terms of the beta function. We describe the evaluation of some of them.
This work is devoted to the investigation of the quantum mechanical systems on the two dimensional hyperboloid which admit separation of variables in at least two coordinate systems. Here we consider two potentials introduced in a paper of…
The authors survey recent results in special functions of classical analysis and geometric function theory, in particular the circular and hyperbolic functions, the gamma function, the elliptic integrals, the Gaussian hypergeometric…
A generalization of the quotient integral formula is presented and some of its properties are investigated. Also the relations between two function spaces related to the spacial homogeneous spaces are derived by using general quotient…
We use the method of brackets to evaluate quadratic and quartic type integrals. We recall the operational rules of the method and give examples to illustrate its working. The method is then used to evaluate the quadratic type integrals…
In the paper, the authors prove that the generalized sine function $\sin_{p,q}(x)$ and the generalized hyperbolic sine function $\sinh_{p,q}(x)$ are geometrically concave and geometrically convex, respectively. Consequently, the authors…
We construct the geometric quantization of a compact surface using a singular real polarization coming from an integrable system. Such a polarization always has singularities, which we assume to be of nondegenerate type. In particular, we…
The main aim of this note, which can be viewed as a certain addendum to the paper \cite{2019}, is to propose several generalized inequalities for the ratio functions of trigonometric and hyperbolic functions. We basically follow the…
We survey the properties of Brody and Kobayashi hyperbolic manifolds.
In this article we give evaluations of certain series of hyperbolic functions, using Jacobi elliptic functions theory. We also define some new functions that enable us to give characterization of not solvable class of series.
This article addresses linear hyperbolic partial differential equations and pseudodifferential equations with strongly singular coefficients and data, modelled as members of algebras of generalised functions. We employ the recently…
We consider certain double series of Eisenstein type involving hyperbolic-sine functions. We define certain generalized Hurwitz numbers, in terms of which we evaluate those double series. Our main results can be regarded as a certain…
This paper investigates a class of special Berndt-type integral calculations where the integrand contains only hyperbolic cosine functions. The research approach proceeds as follows: Firstly, through contour integration methods, we…
In this paper we provided a classification for partitions of intervals on the hyperbolic plane. Given a partition, to be named strong, we define a notion of a hyperbolic-valued functions of bounded variation and a kind of Riemann-Stieltjes…
In this paper some concepts of convex analysis on hyperbolic space are studied. We first study properties of the intrinsic distance, for instance, we present the spectral decomposition of its Hessian. Next, we study the concept of convex…
In math.QA/0309252, the author proved a number of multivariate elliptic hypergeometric integrals. The purpose of the present note is to explore more carefully the various limiting cases (hyperbolic, trigonometric, rational, and classical)…
In this article, we construct partial periodic quotients of groups which have a non-elementary acylindrical action on a hyperbolic space. In particular, we provide infinite quotients of mapping class groups where a fixed power of every…
We generalize several integrals studied by Glaisher. These ideas are then applied to obtain an analog of an integral due to Ismail and Valent.