35 citations · 192 across the 23 of their papers we have counts for
25 papers
Polynomials and asymptotic constants in a resurgent problem from 't Hooft
David Broadhurst, Gergő Nemes
In a recent study of the quantum theory of harmonic oscillators, Gerard 't Hooft proposed the following problem: given for , find its a…
Hyperasymptotics for linear difference equations with an irregular singularity of rank one: Polynomial coefficients
Gergő Nemes
Hyperasymptotics is an analytical method that incorporates exponentially small contributions into asymptotic approximations, thereby expanding their domain of validity, improving a…
Smoothing of the higher-order Stokes phenomenon
Chris J. Howls, John R. King, Gergő Nemes +1
For nearly a century and a half the Stokes phenomenon had been perceived as a discontinuous change in the asymptotic representation of a function. In 1989 Berry demonstrated how it…
Simple error bounds for an asymptotic expansion of the partition function
Gergő Nemes
Recently, there has been renewed interest in studying the asymptotic properties of the integer partition function . Hardy, Ramanujan, and Rademacher provided detailed asympto…
Dingle's final main rule, Berry's transition, and Howls' conjecture
Gergő Nemes
The Stokes phenomenon is the apparent discontinuous change in the form of the asymptotic expansion of a function across certain rays in the complex plane, known as Stokes lines, as…
Error bounds for the asymptotic expansions of the Hermite polynomials
Wei Shi, Gergő Nemes, Xiang-Sheng Wang +1
In this paper, we present explicit and computable error bounds for the asymptotic expansions of the Hermite polynomials with Plancherel--Rotach scale. Three cases, depending on whe…
Asymptotic expansions for the incomplete gamma function in the transition regions
Gergő Nemes, Adri B. Olde Daalhuis
We construct asymptotic expansions for the normalised incomplete gamma function that are valid in the transition regions, including the case , and…
An extension of Laplace's method
Gergő Nemes
Asymptotic expansions are obtained for contour integrals of the form \[ \int_a^b \exp \left( - zp(t) + z^{ν/μ} r(t) \right)q(t)dt, \] in which is a large real or complex parame…
Globally exact asymptotics for integrals with arbitrary order saddles
Thomas Bennett, Christopher J. Howls, Gergő Nemes +1
We derive the first exact, rigorous but practical, globally valid remainder terms for asymptotic expansions about saddles and contour endpoints of arbitrary order degeneracy derive…
Error bounds for the large-argument asymptotic expansions of the Lommel and allied functions
Gergő Nemes
In this paper, we reconsider the large- asymptotic expansion of the Lommel function and its derivative. New representations for the remainder terms of the asymptoti…
Error bounds for the asymptotic expansion of the Hurwitz zeta function
Gergő Nemes
In this paper, we reconsider the large- asymptotic expansion of the Hurwitz zeta function . New representations for the remainder term of the asymptotic expansion are fo…
Uniform Asymptotic Expansion for the Incomplete Beta Function
Gergő Nemes, Adri B. Olde Daalhuis
In [Temme N.M., Special functions. An introduction to the classical functions of mathematical physics, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1996, Se…
Error bounds for the large-argument asymptotic expansions of the Hankel and Bessel functions
Gergő Nemes
In this paper, we reconsider the large-argument asymptotic expansions of the Hankel, Bessel and modified Bessel functions and their derivatives. New integral representations for th…
The resurgence properties of the Incomplete gamma function II
Gergő Nemes
In this paper we derive a new representation for the incomplete gamma function, exploiting the reformulation of the method of steepest descents by C. J. Howls (Howls, Proc. R. Soc.…
The resurgence properties of the incomplete gamma function I
Gergő Nemes
In this paper we derive new representations for the incomplete gamma function, exploiting the reformulation of the method of steepest descents by C. J. Howls (Howls, Proc. R. Soc.…
The resurgence properties of the Hankel and Bessel functions of nearly equal order and argument
Gergő Nemes
The aim of this paper is to derive new representations for the Hankel functions, the Bessel functions and their derivatives, exploiting the reformulation of the method of steepest…
Error bounds and exponential improvement for the asymptotic expansion of the Barnes -function
Gergő Nemes
In this paper we establish new integral representations for the remainder term of the known asymptotic expansion of the logarithm of the Barnes -function. Using these representa…
On the large argument asymptotics of the Lommel function via Stieltjes transforms
Gergő Nemes
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 pr…
The resurgence properties of the large order asymptotics of the Anger--Weber function II
Gergő Nemes
In this paper, we derive a new representation for the Anger--Weber function, employing the reformulation of the method of steepest descents by C. J. Howls (Howls, Proc. R. Soc. Lon…
The resurgence properties of the large order asymptotics of the Anger--Weber function I
Gergő Nemes
The aim of this paper is to derive new representations for the Anger--Weber function, exploiting the reformulation of the method of steepest descents by C. J. Howls (Howls, Proc. R…
Error bounds and exponential improvements for the asymptotic expansions of the gamma function and its reciprocal
Gergő Nemes
In (Boyd, Proc. R. Soc. Lond. A 447 (1994) 609--630), W. G. C. Boyd derived a resurgence representation for the gamma function, exploiting the reformulation of the method of steepe…
The resurgence properties of the large order asymptotics of the Hankel and Bessel functions
Gergő Nemes
The aim of this paper is to derive new representations for the Hankel and Bessel functions, exploiting the reformulation of the method of steepest descents by M. V. Berry and C. J.…
An explicit formula for the coefficients in Laplace's method
Gergő Nemes
Laplace's method is one of the fundamental techniques in the asymptotic approximation of integrals. The coefficients appearing in the resulting asymptotic expansion, arise as the c…
A solution to an open problem on the Mathieu series posed by Hoorfar and Qi
Gergő Nemes
In this paper, the author gives a solution to an open problem about the famous Mathieu series, that is, he obtains a sharp double inequality for bounding this series.