Related papers: The Maillet--Malgrange type theorem for generalize…
From physical perspective, derivatives can be viewed as mathematical idealizations of the linear growth. The linear growth condition has special properties, which make it preferred. The manuscript investigates the general properties of the…
We describe partial differential operators for which we can construct generalised integral means satisfying Pizzetti-type formulas. Using these formulas we give a new characterisation of summability of formal power series solutions to some…
The fundamental theorem of tropical differential algebra has been established for formal power series solutions of systems of algebraic differential equations. It has been shown that the direct extension to formal Puiseux series solutions…
The generalized number-theoretic transformation (NPT) is formulated on the basis of the exponential function theorem, which allows us to replace operations modulo the expression as a whole by modulo operations on the exponent of this…
The principal aim of this paper is to establish a purity theorem for Mahler functions that is reminiscent of famous purity theorems for G-functions by D. and G. Chudnovsky and for E-functions (and, more generally, for holonomic arithmetic…
In this paper, we investigate the Euler-type integral representations for the generalized hypergeometric matrix function and develop some transformations in terms of hypergeometric matrix functions. Furthermore, unit and half arguments have…
We establish a Liouville type theorem for some conformally invariant fully nonlinear equations
The article presents mathematical generalization of results which originated as solutions of practical problems, in particular, the modeling of transitional processes in electrical circuits and problems of resource allocation. However, the…
We propose a sufficient condition of the convergence of a complex power type formal series of the form $\varphi=\sum_{k=1}^{\infty}\alpha_k(x^{{\rm i}\gamma})\,x^k$, where $\alpha_k$ are functions meromorphic at the origin and…
Starting from the expression for the superdeterminant of (xI-M), where M is an arbitrary supermatrix, we propose a definition for the corresponding characteristic polynomial and we prove that each supermatrix satisfies its characteristic…
This paper studies the equivalence between generalized holomorphic functions (GHF) and complex analytic functions in the framework of Robinson-Colombeau generalized numbers. In every non-Archimedean ring, the use of ordinary series is…
Under integral restrictions on dilatations, it is proved existence theorems for the degenerate Beltrami equations with two characteristics and, in particular, to the Beltrami equations of the second type that play a great role in many…
Based on previous work we consturct an equation (Lagrange equation) and relate it with a system of generalized integrals and differential equations in such a way to provide useful evaluations and connections between them.
By making use of the familiar Mathieu series and its generalizations, the authors derive a number of new integral representations and present a systematic study of probability density functions and probability distributions associated with…
We show generic existence of power series a with complex coefficients a_n, such that the sequence of partial sums of a new power series where its coefficients b_n are functions of a_0, a_1, ..., a_n approximate every polynomial uniformly on…
We prove a generalization of Gabrielov's rank theorem for families of rings of power series which we call W-temperate. Examples include the families of complex analytic functions and of Eisenstein series. As a Corollary, we provide rank…
Algebraic power series are formal power series which satisfy a univariate polynomial equation over the polynomial ring in n variables. This relation determines the series only up to conjugacy. Via the Artin-Mazur theorem and the implicit…
Several examples of generalized number systems are constructed to compare various conditions occurring in the literature for the prime number theorem in the context of Beurling generalized primes.
We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.
Motivated by two Legendre-type formulas for overpartitions, we derive a variety of their companions as Legendre theorems for overpartition pairs. This leads to equalities of subclasses of overpartitions and overpartition pairs.