Related papers: Convergence in $\C$ of series for the Lambert $W$ …
The paper introduces a new concept of $\Lambda $-variation of multivariable functions and investigates its connection with the convergence of multidimensional Fourier series
We study the questions of determining the asymptotics of the probabilistic characteristics of additive arithmetic functions in the paper, regardless of whether they have a limit distribution or not. Several assertions are proved about the…
Recently, symbolic regression (SR) has demonstrated its efficiency for discovering basic governing relations in physical systems. A major impact can be potentially achieved by coupling symbolic regression with asymptotic methodology. The…
In this paper, under certain restrictions on linear factors of the denominator of a rational function of two variables, the leading term of the asymptotic expansion of the coefficients is found.
The $\psi(x)$-function, which solves the equation $x = \sinh(aw)e^w$ for $0<a<1$, has a natural connection to the renowned Lambert $W$ function and also physical relevance through its connection to the Lenz-Ising model of ferromagnetism. We…
This is my dissertation. Its research object is a symmetric group of permutations acting on a finite set. The density of permutations with a given cycle structure pattern is explored when the group order tends to infinity. New and sharper…
We construct asymptotic expansions for the normalised incomplete gamma function $Q(a,z)=\Gamma(a,z)/\Gamma(a)$ that are valid in the transition regions, including the case $z\approx a$, and have simple polynomial coefficients. For Bessel…
We derive the asymptotic expansion (asymptotics with an arbitrary number of error terms) of k-regular graphs by applying the Laplace method on a recent exact formula from Caizergues and de Panafieu (2023). We also deduce the asymptotic…
In this work, we introduce the notion of Gevrey asymptotic expansion and we show how the classical concept of a convergent power series can be generalized to include the case in which the radius of convergence is zero. This technique can be…
Slowly convergent series and sequences as well as divergent series occur quite frequently in the mathematical treatment of scientific problems. In this report, a large number of mainly nonlinear sequence transformations for the acceleration…
An extension of the finite and infinite Lie groups properties of complex numbers and functions of complex variable is proposed. This extension is performed exploiting hypercomplex number systems that follow the elementary algebra rules. In…
Using a differential equation approach asymptotic expansions are rigorously obtained for Lommel, Weber, Anger-Weber and Struve functions, as well as Neumann polynomials, each of which is a solution of an inhomogeneous Bessel equation. The…
Some special functions are particularly relevant in applied probability and statistics. For example, the incomplete beta function is the cumulative central beta distribution. In this paper, we consider the inversion of the central…
We consider a class of nonparametric time series regression models in which the regressor takes values in a sequence space. Technical challenges that hampered theoretical advances in these models include the lack of associated Lebesgue…
This paper is concerned with investigating the asymptotic behavior of the gradients of solutions to a class of elliptic systems with general boundary data, especially covering the Lam\'{e} systems, in a narrow region. The novelty of this…
We make use of Friedrich's representation of spatial infinity to study asymptotic expansions of the Maxwell-scalar field system near spatial infinity. The main objective of this analysis is to understand the effects of the non-linearities…
Recently, the complete left tail asymptotic for the density of the {\it martingale limit} of the classical Galton-Watson process has been derived. The derivation is based on the properties of a special function (whose inverse Fourier…
Classical mathematical statistics deals with models that are parametrized by a Euclidean, i.e. finite dimensional, parameter. Quite often such models have been and still are chosen in practical situations for their mathematical simplicity…
The right tail asymptotic series consisting of attenuating exponential terms are derived for the densities of Galton-Watson processes with fractional probability generating functions. The frequencies in the exponential factors form fractal…
In this paper we give a bound for the Iwasawa lambda invariant of an abelian number field attached to the cyclotomic Z_p-extension of that field. We also give some properties of Iwaswa power series attached to p-adic L-functions.