Related papers: Asymptotic analysis of symmetric functions
This paper is a short overview of the main Abelian- and Tauberian-type results from [4, 14, 26] regarding the asymptotic analysis of different classes of generalized functions in terms of appropriate frames. The Tauberian-type results…
In this paper we present a complete asymptotic expansion of a symmetric homogeneous stable (balanced), stabilizable and stabilized mean. By including known asymptotic expansions of parametric means it is shown how the obtained coefficients…
Asymptotic expansions of series $\sum_{k=0}^\infty \epsilon^k(k+a)^\gamma e^{-(k+a)^\alpha x}$ and $\sum_{k=0}^\infty \epsilon^k(k+a)^\gamma / (x(k+a)^\alpha+1)^\mu}$ in powers of $x$ as $x\to+0$ are found, where $\epsilon=1$ or…
The Cantor ladder is naturally included into various families of self-similar functions. In the frame of these families we study the asymptotics of some parametric integrals.
Some properties of integral averages of functions on intervals and their asymptotic behavior are investigated. The results are aimed at applications to entire and subharmonic functions.
Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…
The paper explores various special functions which generalize the two-parametric Mittag-Leffler type function of two variables. Integral representations for these functions in different domains of variation of arguments for certain values…
This paper deals with asymptotics for multiple-set linear canonical analysis (MSLCA). A definition of this analysis, that adapts the classical one to the context of Euclidean random variables, is given and properties of the related…
We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms, focussing on the case of multiple, non-commensurate frequencies. We derive an asymptotic expansion in inverse powers of the…
Asymptotic almost automorphy is introduced and studied in the context of some algebras of generalized functions. We also give applications to neutral difference differential systems in the framework of such generalized functions.
An asymptotic expansion for a ratio of products of gamma functions is derived.
The aim of this work is to analyze general infinite sums containing modified Bessel functions of the second kind. In particular we present a method for the construction of a proper asymptotic expansion for such series valid when one of the…
General results on asymptotic expansions of Feynman diagrams in momenta and/or masses are reviewed. It is shown how they are applied for calculation of massive diagrams.
The paper considers a universal approach that allows one to quite simply obtain nonlinear asymptotic estimates of various summation functions. It is shown the application of this approach to the asymptotic estimation of divergent Dirichlet…
Integral representations play a prominent role in the analysis of entire functions. The representations of generalized Mittag-Leffler type functions and their asymptotics have been (and still are) investigated by plenty of authors in…
On the set $\mathcal M$ of mean functions the symmetric mean of $M$ with respect to mean $M_0$ can be defined in several ways. The first one is related to the group structure on $\mathcal M$ and the second one is defined trough Gauss'…
Some problems in the theory and applications of stochastic processes can be reduced to solving integral equations. While explicit solutions for these equations are often elusive, valuable insights can be gained through their asymptotic…
Convergence rate estimates in limit theorems for sums of independent random variables are considered.
We study the structure of the asymptotic expansion of the probability that a combinatorial object is connected. We show that the coefficients appearing in those asymptotics are integers and can be interpreted as the counting sequences of…