Related papers: Normality criteria concerning composite meromorphi…
We introduce a new family of symmetric multivariate polynomials, whose coefficients are meromorphic functions of two parameters $(q,t)$ and polynomial in a further two parameters $(u,v)$. We evaluate these polynomials explicitly as a matrix…
Let F be a family of functions meromorphic in a domain D. If {|f|/(1+|f|^3):f in F} is locally uniformly bounded away from zero, then F is normal.
We show that a family of meromorphic functions in the unit disk $\dk$ whose spherical derivatives are uniformly bounded away from zero is normal. Furthermore, we show that for each $f$ meromorphic in $\dk$ we have $\inf_{z\in\dk} f^#(z)\le…
The probability content of a convex polyhedron with a multivariate normal distribution can be regarded as a real analytic function. We give a system of linear partial differential equations with polynomial coefficients for the function and…
In this paper, we survey and study definitions and properties of tropical polynomials, tropical rational functions and in general, tropical meromorphic functions, emphasizing practical techniques that can really carry out computations. For…
The aim of this paper is to consider the value distribution of a differential monomial generated by a transcendental meromorphic function.
This paper extends earlier work on the distribution in the complex plane of the roots of random polynomials. In this paper, the random polynomials are generalized to random finite sums of given "basis" functions. The basis functions are…
The goal of this paper is to classify pairs of Morse functions in general position modulo the action of different groups.In particular, we obtain the classification of generic pairs of Morse functions, with or without target…
In a previous paper the authors elaborated notions and technique which could be applied to compute such invariants of polynomials as Euler characteristics of fibres and zeta-functions of monodromy transformations associated with a…
In this paper our aim is to extend and improve the sufficient conditions for integral operators involving the normalized forms of the generalized Bessel functions of the first kind to be univalent in the open unit disk as investigated…
We give an elementary characterization of rational functions among meromorphic functions in the complex plane.
We use discrete holomorphic polynomials to prove that, given a refining sequence of critical maps of a Riemann surface, any holomorphic function can be approximated by a converging sequence of discrete holomorphic functions.
Let $f$ be a transcendental meromorphic function, defined in the complex plane $\mathbb{C}$. In this paper, we give a quantitative estimations of the characteristic function $T(r,f)$ in terms of the counting function of a homogeneous…
Let $\{f_{\lambda; j}\}_{\lambda\in V; 1\le j\le k}$ be families of holomorphic functions in the open unit disk $\Di\subset\Co$ depending holomorphically on a parameter $\lambda\in V\subset \Co^n$. We establish a Rolle type theorem for the…
In this article, we give a Zalcman type renormalization result for the quasinormality of a family of holomorphic functions on a domain in $\mathbb{C}^n$ that takes values in a complete complex Hermitian manifold.
The purpose of this work is to analyse a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes an additional term on the sphere. First, we will get connection formulas relating classical…
In this paper, we investigated the Fourier partial sums with respect to general orthonormal systems when the function $f$ belongs to some differentiable class of functions
In the paper, concerning a question of Yi [23], we study general criterion for the uniqueness of an L-function and a general meromorphic function. Our results improve and extend all the existing results in this direction [23, 18, 17, 4] to…
In this paper we consider generalized monomial functions $f, g\colon \mathbb{F}\to \mathbb{C}$ (of possibly different degree) that also fulfill \[ f(P(x))= Q(g(x)) \qquad \left(x\in \mathbb{F}\right), \] where $P\in \mathbb{F}[x]$ and $Q\in…
This work presents a family of fiber bundles where the total spaces are associated with holomorphic functions on several complex variables and the basis spaces extend the notion of quaternionic slice regular functions of several…