Related papers: Asymptotics for a certain group of exponential gen…
We study the asymptotic behaviour of a real-valued diffusion whose non-regular drift is given as a sum of a dissipative term and a bounded measurable one. We prove that two trajectories of that diffusion converge a.s. to one another at an…
Given an o-minimal expansion $\mathbb{R}_{\mathcal{A}}$ of the real ordered field, generated by a generalized quasianalytic class $\mathcal{A}$, we construct an explicit truncation closed ordered differential field embedding of the Hardy…
In this work a method is presented to derive the generating functional in path integral form for a system with an arbitrary number of degrees of freedom and constrained by general conditions. The method is applied to the case of the…
The two regular super-exponentials to base exp(1/e) are constructed. An efficient algorithm for the evaluation of these super-exponentials and their inverse functions is suggested and compared to the already published results.
An asymptotic expansion for the generalised quadratic Gauss sum $$S_N(x,\theta)=\sum_{j=1}^{N} \exp (\pi ixj^2+2\pi ij\theta),$$ where $x$, $\theta$ are real and $N$ is a positive integer, is obtained as $x\rightarrow 0$ and…
Asymptotic properties of certain arithmetic functions involving exponential divisors are investigated.
Motivated by the convolutive behavior of the counting function for partitions with designated summands in which all parts are odd, we consider coefficient sequences $(a_n)_{n\ge 0}$ of primitive eta-products that satisfy the generic…
We investigate the asymptotic expansion of integrals analogous to Ball's integral \[\int_0^\infty \left(\frac{\Gamma(1+\nu)|J_\nu(x)|}{(x/2)^\nu}\right)^{\!n}dx\] for large $n$ in which the Bessel function $J_\nu(x)$ is replaced by the…
The main aim of this article is to characterize and investigate the three parameter exponentiated exponential Poisson probability distribution ${\rm EEP}(\alpha, \beta, \lambda)$ by giving explicit closed form expressions for its…
This work gives a general approach to the determination of the asymptotic behavior of the sums of functions of primes based on the distribution of primes. It refines the estimate of the remainder term of the asymptotic expansion of the sums…
Abel's functional equation for $2^{x/2}$ and half-iterates of $\lambda x (1-x)$ & $\sqrt{1+x}$ are featured in this collection of exercises ($0 < \lambda \neq 1 < 2$).
We examine convergent representations for the sum of a decaying exponential and a Bessel function in the form \[\sum_{n=1}^\infty \frac{e^{-an}}{(\frac{1}{2} bn)^\nu}\,J_\nu(bn),\] where $J_\nu(x)$ is the Bessel function of the first kind…
The results of part I (hep-ph/9612284) are used to obtain full asymptotic expansions of Feynman diagrams renormalized within the MS-scheme in the regimes when some of the masses and external momenta are large with respect to the others. The…
We consider a multivariate generating function F(z), whose coefficients are indexed by d-tuples of nonnegative integers: F(z) = sum_r a_r z^r where z^r denotes the product of z_j^{r_j} over j = 1, ..., d. Suppose that F(z) is meromorphic in…
We study the leading coefficient in the asymptotical formula $ N (R) = \frac{W}{\pi} R + O (1) $, $ R \to \infty $, for the resonance counting function $ N (R)$ of Schr\"odinger Hamiltonians with point interactions. For such Hamiltonians,…
Let \sum_{n\in N^d} f_{n_1, ..., n_d} x_1^{n_1}... x_d^{n_d} be a multivariate generating function that converges in a neighborhood of the origin of C^d. We present a new, multivariate method for computing the asymptotics of the diagonal…
This paper establishes new results concerning asymptotic expansions of $q$-series related to partial theta functions. We first establish a new method to obtain asymptotic expansions using a result of Ono and Lovejoy, and then build on these…
The generating function and an explicit expression is derived for the (colored) Motzkin numbers of higher rank introduced recently. Considering the special case of rank one yields the corresponding results for the conventional colored…
Let G be a finite additive abelian group with exponent exp(G)=n>1 and let A be a nonempty subset of {1,...,n-1}. In this paper, we investigate the smallest positive integer $m$, denoted by s_A(G), such that any sequence {c_i}_{i=1}^m with…
We are interested in the asymptotic behavior of orthogonal polynomials of the generalized Jacobi type as their degree $n$ goes to $\infty$. These are defined on the interval $[-1,1]$ with weight function…