Related papers: Asymptotic evaluation of a function defined by pow…
A novel method of summation for power series is developed. The method is based on the self-similar approximation theory. The trick employed is in transforming, first, a series expansion into a product expansion and in applying the…
Asymptotic expansion is presented for an estimator of the Hurst coefficient of a fractional Brownian motion. For this, a recently developed theory of asymptotic expansion of the distribution of Wiener functionals is applied. The effects of…
We give an overview of basic methods that can be used for obtaining asymptotic expansions of integrals: Watson's lemma, Laplace's method, the saddle point method, and the method of stationary phase. Certain developments in the field of…
The standard approach to analyzing the asymptotic complexity of probabilistic programs is based on studying the asymptotic growth of certain expected values (such as the expected termination time) for increasing input size. We argue that…
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…
We present expressions for the coefficients which arise in asymptotic expansions of multiple integrals of Laplace type (the first term of which is known as Laplace's approximation) in terms of asymptotic series of the functions in the…
We examine the sum of modified Bessel functions with argument depending quadratically on the summation index given by \[S_\nu(a)=\sum_{n\geq 1} (\frac{1}{2} an^2)^{-\nu} K_\nu(an^2)\qquad (|\arg\,a|<\pi/2)\] as the parameter $|a|\to 0$. It…
Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…
Inequalities, asymptotics and, for some specific cases, asymptotical expansions were obtained for generalized Mathieu's series. A connection between inequalities for Mathieu's series and positive definite and completely monotonic functions.
In this paper, we obtain asymptotic formulas for an infinite class of rank generating functions. As an application, we solve a conjecture of Andrews and Lewis on inequalities between certain ranks.
We define a type of generalized asymptotic series called $v$-asymptotic. We show that every function with moderate growth at infinity has a $v$-asymptotic expansion. We also describe the set of $v$-asymptotic series, where a given function…
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…
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…
Using a recently derived integral in terms of elementary functions, we derive new asymptotic expansions of the normal inverse Gaussian cumulative distribution function. One of the asymptotic representations is in terms of the normal…
We study the distribution of partition parts in arithmetic progressions and find asymptotic results that capture all exponentially growing terms. This is accomplished by studying the behavior of non-modular Eisenstein series that appear in…
The aim of this work is to expose some asymptotic series associated to some expressions involving the volume of the n-dimensional unit ball. All proofs and the methods used for improving the classical inequalities announced in the final…
We derive an asymptotic expansion for the Weyl function of a one-dimensional Schr\"odinger operator which generalizes the classical formula by Atkinson. Moreover, we show that the asymptotic formula can also be interpreted in the sense of…
The problem of asymptotic expansions of Green functions in perturbative QFT is studied for the class of Euclidean asymptotic regimes. Phenomenological applications are analyzed to obtain a meaningful mathematical formulation of the problem.…
In this paper, we provide a rigorous derivation of asymptotic formula for the largest eigenvalues using the convergence estimation of the eigenvalues of a sequence of self-adjoint compact operators of perturbations resulting from the…
A new effective method for factorization of a class of nonrational $n\times n$ matrix-functions with \emph{stable partial indices} is proposed. The method is a generalization of the one recently proposed by the authors which was valid for…