Related papers: Asymptotics for a Variant of the Mittag-Leffler Fu…
We prove a version of the classical Mittag-Leffler Theorem for regular functions over quaternions. Our result relies upon an appropriate notion of principal part, that is inspired by the recent definition of spherical analyticity.
In this article we consider fractional Laplacians which seem to be of interest to probability theory. This is a rather new class of operators for us but our methods works (with a twist, as usual). Our main goal is to derive a two-term…
Generalization of the integral representation of the gamma function has been obtained, which shows that the Hankel contour assumes rotation in the complex plane. The range of admissible values for the contour rotation angle is set. Using…
A generalization of the Emden-Fowler equation is presented and its solutions are investigated. This paper is devoted to asymptotic behavior of its solutions. The procedure is entirely based on a previous paper by the author.
Using a modified version of Schauder's fixed point theorem, measures of non-compactness and classical techniques, we provide new general results on the asymptotic behavior and the non-oscillation of second order scalar nonlinear…
We address the problem of ambiguity of a function determined by an asymptotic perturbation expansion. Using a modified form of the Watson lemma recently proved elsewhere, we discuss a large class of functions determined by the same…
Asymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given…
In this paper we tackle the asymptotic behavior of a family of orthogonal polynomials with respect to a nonstandard inner product involving the forward operator {\Delta}. Concretely, we treat the generalized Charlier weights in the…
An asymptotic expansion formula of Riemann sums over lattice polytopes is given. The formula is an asymptotic form of the local Euler-Maclaurin formula due to Berline-Vergne. The proof given here for Delzant lattice polytopes is independent…
We obtain the asymptotic expansion for large integer $n$ of a generalised sine-integral \[\int_0^\infty\left(\frac{\sin\,x}{x}\right)^{n}dx\] by utilising the saddle-point method. This expansion is shown to agree with recent results of J.…
We propose a refined version of the existing conjectural asymptotic formula for the moments of the family of quadratic Dirichlet L-functions over rational function fields. Our prediction is motivated by two natural conjectures that provide…
Recently there has been a renewed interest in asymptotic Euler-MacLaurin formulas, partly due to applications to spectral theory of differential operators. Using elementary means, we recover such formulas for compactly supported smooth…
Simple unsmoothed formulas to compute the Riemann zeta function, and Dirichlet $L$-functions to a power-full modulus, are derived by elementary means (Taylor expansions and the geometric series). The formulas enable square-root of the…
In this paper we consider the strong asymptotic behavior of Laguerre polynomials in the complex plane. The leading behavior is well known from Perron and Mehler-Heine formulas, but higher order coefficients, which are important in the…
The aim of this paper is to investigate in detail the known large argument asymptotic series of the Lommel function by Stieltjes transform representations. We obtain a number of properties of this asymptotic expansion, including explicit…
We establish a new generalized Taylor's formula for power fractional derivatives with nonsingular and nonlocal kernels, which includes many known Taylor's formulas in the literature. Moreover, as a consequence, we obtain a general version…
We prove an Asymptotic Implicit Function Theorem in the setting of Gevrey asymptotics with respect to a parameter. The unique implicitly defined solution admits a Gevrey asymptotic expansion and furthermore it is the Borel resummation of…
Let $F(x)= \sum_{\nu\in\NN^d} F_\nu x^\nu$ be a multivariate power series with complex coefficients that converges in a neighborhood of the origin. Assume $F=G/H$ for some functions $G$ and $H$ holomorphic in a neighborhood of the origin.…
The classical Stirling's formula gives the asymptotic behavior of the gamma function. Katayama and Ohtsuki generalized this formula for Barnes' multiple gamma functions. In this paper, we further generalize these formulas for the multiple…
Improving earlier work of Balasubramanian, Conrey and Heath-Brown, we obtain an asymptotic formula for the mean-square of the Riemann zeta-function times an arbitrary Dirichlet polynomial of length $T^{1/2 + \delta}$, with $\delta =…