Related papers: A new generalization of generalized hypergeometric…
Generalised Hermite-Gaussian modes (gHG modes), an extended notion of Hermite-Gaussian modes (HG modes), are formed by the summation of normal HG modes with a characteristic function $\alpha$, which can be used to unite conventional HG…
We present a generalization of Schlick's bias and gain functions -- simple parametric curve-shaped functions for inputs in [0, 1]. Our single function includes both bias and gain as special cases, and is able to describe other smooth and…
In this article, we define a new class of convexity called generalized $(h-m)$-convexity, which generalizes $h$-convexity and $m$-convexity on fractal sets $\mathbb{R}^{\alpha}$ $(0<\alpha\leq 1)$. Some properties of this new class are…
We consider different generalizations of the Euler formula and discuss the properties of the associated trigonometric functions. The problem is analyzed from different points of view and it is shown that it can be formulated in a natural…
In this work we introduce a new algebra of tempered generalized functions. The tempered distributions are embedded in this algebra via their Hermite expansions. The Fourier transform is naturally extended to this algebra in such a way that…
The 15 Gauss contiguous relations for ${}_2F_1$ hypergeometric series imply that any three ${}_2F_1$ series whose corresponding parameters differ by integers are linearly related (over the field of rational functions in the parameters). We…
A generalized matrix function is a generalization of determinant and permanent function. In this paper, we introduced the formula for the value of a generalized matrix function of a linear sum of permutation matrices. We show that a linear…
This paper shows that certain $\,_{3}F_{4}$ hypergeometric functions may be expanded in sums of pair products of $\,_{2}F_{3}$ functions. This expands the class of hypergeometric functions having summation theorems beyond those expressible…
In this paper, we consider the generating functions of the complete and elementary symmetric functions and provide a new generalization of these classical symmetric functions. Some classical relationships involving the complete and…
In this paper, we give an algorithm to generate connection formulas of generalized hypergeometric functions ${}_p F_{p-1}$ for degenerated values of parameters. We also show that these connection formulas give a fast method for numerical…
Euler defines a function f(x) somehow as an infinite product and a generalization of [x], where [x] ist, what we now call following Legendre the Gamma-Funktion. He gets some recursive relationships for f(x), by applying some very nice…
In this paper, we investigate the relationships among hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions through some families of `hypergeometric' algebraic varieties that are higher dimensional…
The aim of this paper is to generalize the Hermite--Hadamard inequality for functions convex on the coordinates. Our composite result generalizes the result of Dragomir in \cite{Drag}. Many other interesting inequalities can be derived from…
We revisit the S-procedure for general functions with "geometrical glasses". We thus delineate a necessary condition, and almost a sufficient condition, to have the S-procedure valid. Everything is expressed in terms of convexity of…
The A-hypergeometric system studied by I.M. Gelfand, M.I. Graev, A.V. Zelevinsky and the author, is defined for a set A of characters of an algebraic torus. In this paper we propose a generalization of the theory where the torus is replaced…
In this paper, we prove that transnormal functions are isoparametric functions on Finsler space forms (N(c), F) under certain conditions, which generalize Theorem B given by Q.M. Wang in Riemannian case. Next, we discuss the relationship…
In this article we give an example of a matrix version of the famous congruence for hypergeometric functions found by Dwork in 'p-adic cycles'.
We show how certain hypergeometric functions play an important role in finding fundamental solutions for a generalized Tricomi operator.
This paper deals with a new kind of generalized functions, called "ultrafunctions" which have been introduced recently and developed in some previous works. Their peculiarity is that they are based on a Non-Archimedean field namely on a…
The purpose of this work is to introduce a general class of $C_G$-simulation functions and obtained some new coincidence and common fixed points results in metric spaces. Some useful examples are presented to illustrate our theorems.…