Related papers: The Parabolic-Trigonometric Functions
In this paper we review and derive hyperbolic and trigonometric double summation addition theorems for Jacobi functions of the first and second kind. In connection with these addition theorems, we perform a full analysis of the relation…
We calculate the Jacobian matrix of the dihedral angles of a generalized hyperbolic tetrahedron as functions of edge lengths and find the complete set of symmetries of this matrix.
General elliptic hypergeometric functions are defined by elliptic hypergeometric integrals. They comprise the elliptic beta integral, elliptic analogues of the Euler-Gauss hypergeometric function and Selberg integral, as well as elliptic…
The so-called polynomial equations play an important role both in algebra and in the theory of functional equations. If the unknown functions in the equation are additive, relatively many results are known. However, even in this case, there…
We introduce a parabolic version of the so-called John-Nirenberg space that is a generalization of functions of parabolic bounded mean oscillation. Parabolic John-Nirenberg inequalities, which give weak type estimates for the oscillation of…
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…
This article presents a comprehensive overview and supplement to recent developments in second-order elliptic partial differential equations formulated in double divergence form, along with an exploration of their parabolic counterparts.
This article shows how to express relativistic concepts in a visual manner using the full power of hyperbolic trigonometric functions. Minkowski diagrams in energy-momentum space are used in conjunction with hyperbolic triangles. Elegant…
In this paper, authors generalize logarithmic mean $L$, Neuman-S\'andor $M$, two Seiffert means $P$ and $T$ as an application of generalized trigonometric and hyperbolic functions. Moreover, several two-sided inequalities involving these…
After briefly reviewing selected Ising and chiral Potts model results, we discuss a number of properties of cyclic hypergeometric functions which appear naturally in the description of the integrable chiral Potts model and its…
We define and study hyperbolic extensions.
We introduce the notion of orbital L-functions for the space of binary cubic forms and investigate their analytic properties. We study their functional equations and residue formulas in some detail. Aside from the intrinsic interest,…
Special functions have always played a central role in physics and in mathematics, arising as solutions of particular differential equations, or integrals, during the study of particular important physical models and theories in Quantum…
In this paper we prove the conjecture posed by Kl\'en et al. in \cite{kvz}, and give optimal inequalities for generalized trigonometric and hyperbolic functions.
We define SL(r)-opers in the set-up of vector bundles on curves with a parabolic structure over a divisor. Basic properties of these objects are investigated.
Motivated by the work of P. Lindqvist, we study eigenfunctions of the one-dimensional $p$-Laplace operator, the $\sin_p$ functions, and prove several inequalities for these and $p$-analogues of other trigonometric functions and their…
The paper studies complementary choice functions, i.e. monotonic and consistent choice functions. Such choice functions were introduced and used in the work \cite{RY} for investigation of matchings with complementary contracts. Three…
We introduce new p-adic convergent functions, which we call the p-adic hypergeometric functions of logarithmic type. The first main result is to prove the congruence relations that are similar to Dwork's. The second main result is that the…
We discuss a parabolic version of the space of functions of bounded mean oscillation related to a doubly nonlinear parabolic partial differential equation. Parabolic John-Nirenberg inequalities, which give exponential decay estimates for…
We study the convexity properties of the generalized trigonometric functions considered as functions of parameter. We show that $p\to\sin_p(y)$ and $p\to\cos_p(y)$ are log-concave on the appropriate intervals while $p\to\tan_p(y)$ is…