Gergő
Nemes is a research fellow
at the Alfréd Rényi Institute of Mathematics.
He has a Ph.D. degree in Mathematics.
Address:
Alfréd Rényi Institute of
Mathematics
Reáltanoda utca 1315
H1053,
Budapest,
Hungary 
Welcome to my home page. Here
you can find information about my research topics and some of my papers.
I can be contacted by email at nemes.gergo@renyi.hu.
I am currently on leave from the Institute and working at
Tokyo
Metropolitan University.
Research interests:
●
Asymptotic Analysis
●
Écalle Theory
●
Exact WKB Analysis
●
Special Functions
Publications:

On the coefficients of the asymptotic
expansion of n!,
Journal of Integer Sequences
13
(2010), no. 6, Article 10.6.6, 5 pp.

New
asymptotic expansion for the Gamma function,
Archiv der Mathematik
95
(2010), no. 2, 161169

Asymptotic expansion for log n! in terms of the reciprocal of a
triangular number,
Acta Mathematica Hungarica
129
(2010), no. 3, 254262

More accurate approximations for the
Gamma function,
Thai Journal of Mathematics
9
(2011), no. 1, 2128

On the
coefficients of an asymptotic expansion related to Somos' Quadratic
Recurrence Constant,
Applicable Analysis and Discrete Mathematics
5 (2011), no. 1,
6066

An asymptotic expansion for the
Bernoulli Numbers of the Second Kind,
Journal of Integer Sequences
14
(2011), no. 4, Article 11.4.8, 6 pp.

With A. Nemes 
A note on the Landau constants,
Applied Mathematics and Computation
217
(2011), no. 21, 85438546

Proofs of two conjectures on the
Landau constants,
Journal of Mathematical Analysis and Applications
388
(2012), no. 2, 838844

Approximations for the higher order
coefficients in an asymptotic expansion for the Gamma function,
Journal of Mathematical Analysis
and Applications
396
(2012), no. 1, 417424

A remark on some accurate estimates of
p,
Journal of Mathematical
Inequalities
6
(2012), no. 4, 517521

A solution to an open problem on Mathieu series posed by Hoorfar and Qi,
Acta Mathematica Vietnamica
37
(2012), no. 3, 301310

Error bounds and exponential
improvement for Hermite's asymptotic expansion for the Gamma function,
Applicable Analysis and Discrete Mathematics
7
(2013), no. 1, 161179

Generalization of Binet's Gamma
function formulas,
Integral Transforms and Special
Functions
24
(2013), no. 8, 597606

An
explicit formula for the coefficients in Laplace's method,
Constructive Approximation
38
(2013), no. 3, 471487

The resurgence properties of the
largeorder asymptotics of the Hankel and Bessel functions,
Analysis and Applications
12
(2014), no. 4, 403462

The resurgence properties of the
large order asymptotics of the AngerWeber function I,
Journal of Classical Analysis
4
(2014), no. 1, 139

The resurgence properties of the
large order asymptotics of the AngerWeber function II,
Journal of Classical Analysis
4
(2014), no. 2, 121147

Error bounds and exponential
improvement for the asymptotic expansion of the Barnes Gfunction,
Proceedings of the Royal Society A: Mathematical, Physical and Engineering
Sciences
470
(2014), no. 2172, 14 pp.

On the large argument asymptotics of
the Lommel function via Stieltjes transforms,
Asymptotic Analysis
91
(2015), no. 34, 265281

Error
bounds and exponential improvements for the asymptotic expansions of the
gamma function and its reciprocal,
Proceedings of the Royal Society
of Edinburgh, Section A: Mathematics
145
(2015), no. 3, 571596

The resurgence properties of the
incomplete gamma function II,
Studies in Applied
Mathematics
135
(2015), no. 1, 86116

The resurgence properties of the
Hankel and Bessel functions of nearly equal order and argument,
Mathematische Annalen
363 (2015), no. 3, 12071263

The resurgence properties of the
incomplete gamma function I,
Analysis and Applications
14 (2016), no. 5, 631677

With A. B. Olde Daalhuis 
Uniform
asymptotic expansion for the incomplete beta function,
Symmetry, Integrability and Geometry: Methods and Applications
12
(2016), Article 101, 5 pp.

Error
bounds for the largeargument asymptotic expansions of the Hankel and Bessel
functions,
Acta Applicandae Mathematicae 150 (2017), no. 1,
141177

Error
bounds for the asymptotic expansion of the Hurwitz zeta function,
Proceedings of the Royal
Society A: Mathematical, Physical and Engineering Sciences
473 (2017), no. 2203, Article 20170363, 16 pp.

Error bounds
for the largeargument asymptotic expansions of the Lommel and allied
functions,
Studies in Applied Mathematics 140 (2018), no. 4, 508541

With T. Bennett, C. J. Howls, and A.
B. Olde Daalhuis 
Globally
exact asymptotics for integrals with arbitrary order saddles,
SIAM Journal on Mathematical Analysis 50 (2018), no. 2,
21442177

With A. B. Olde Daalhuis 
Asymptotic
expansions for the incomplete gamma function in the transition regions,
Mathematics of Computation 88 (2019), no. 318, 18051827

With A. B. Olde Daalhuis 
Largeparameter
asymptotic expansions for the Legendre and allied functions,
SIAM Journal on Mathematical Analysis 52 (2020), no. 1,
437470

An extension of
Laplace's method,
Constructive Approximation
51 (2020), no. 2, 247272

With Á. Baricz 
Asymptotic
expansions for the radii of starlikeness of normalised Bessel functions,
Journal of Mathematical Analysis and Applications 494 (2021),
no. 2, Article 124624, 11 pp.

On the Borel summability of WKB
solutions of certain Schrödingertype differential equations,
Journal
of Approximation Theory 265 (2021), Article 105562, 30 pp.

Proofs of two conjectures on the
real zeros of the cylinder and Airy functions,
SIAM Journal on Mathematical Analysis 53 (2021), no. 4,
43284349

With W. Shi, X.S. Wang, and R. Wong
 Error bounds
for the asymptotic expansions of the Hermite polynomials,
Proceedings of the Royal Society
of Edinburgh, Section A: Mathematics,
online first

Dingle's final main rule, Berry's
transition, and Howls' conjecture, submitted
The pdf version of my publication
list:
pdf,
and my citation list:
pdf.
My Erdős number is 3.
Curriculum Vitae:
My Curriculum Vitae is avaliable in
pdf.
Ph.D. Dissertation:
My Ph.D. dissertation is avaliable
in
pdf. Errata: pdf.
Notes:
●
A proof of Stirling's formula (in
Hungarian),
2008.
●
Topics in
Combinatorics,
2013.
● Topics
in Algebra (incomplete), 2013.
●
A proof of Burnside's formula,
2017.
Teaching:
Math 5003
(Introduction to Asymptotic Expansions) W 2014
