Gergő
Nemes is a full professor at
Harbin Institute of Technology.
He has a Ph.D. degree in Mathematics.
Address:
Harbin Institute of
Technology
Xidazhi Street, Harbin 150001,
Heilongjiang,
People's Republic of China |
Welcome to my home page. Here
you can find information about my research topics and some of my papers.
I can be contacted by e-mail at
nemes@tmu.ac.jp.
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, 161-169
-
Asymptotic expansion for log n! in terms of the reciprocal of a
triangular number,
Acta Mathematica Hungarica
129
(2010), no. 3, 254-262
-
More accurate approximations for the
Gamma function,
Thai Journal of Mathematics
9
(2011), no. 1, 21-28
-
On the
coefficients of an asymptotic expansion related to Somos' Quadratic
Recurrence Constant,
Applicable Analysis and Discrete Mathematics
5 (2011), no. 1,
60-66
-
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, 8543-8546
-
Proofs of two conjectures on the
Landau constants,
Journal of Mathematical Analysis and Applications
388
(2012), no. 2, 838-844
-
Approximations for the higher order
coefficients in an asymptotic expansion for the Gamma function,
Journal of Mathematical Analysis
and Applications
396
(2012), no. 1, 417-424
-
A remark on some accurate estimates of
p,
Journal of Mathematical
Inequalities
6
(2012), no. 4, 517-521
-
A solution to an open problem on Mathieu series posed by Hoorfar and Qi,
Acta Mathematica Vietnamica
37
(2012), no. 3, 301-310
-
Error bounds and exponential
improvement for Hermite's asymptotic expansion for the Gamma function,
Applicable Analysis and Discrete Mathematics
7
(2013), no. 1, 161-179
-
Generalization of Binet's Gamma
function formulas,
Integral Transforms and Special
Functions
24
(2013), no. 8, 597-606
-
An
explicit formula for the coefficients in Laplace's method,
Constructive Approximation
38
(2013), no. 3, 471-487
-
The resurgence properties of the
large-order asymptotics of the Hankel and Bessel functions,
Analysis and Applications
12
(2014), no. 4, 403-462
-
The resurgence properties of the
large order asymptotics of the Anger-Weber function I,
Journal of Classical Analysis
4
(2014), no. 1, 1-39
-
The resurgence properties of the
large order asymptotics of the Anger-Weber function II,
Journal of Classical Analysis
4
(2014), no. 2, 121-147
-
Error bounds and exponential
improvement for the asymptotic expansion of the Barnes G-function,
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. 3-4, 265-281
-
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, 571-596
-
The resurgence properties of the
incomplete gamma function II,
Studies in Applied
Mathematics
135
(2015), no. 1, 86-116
-
The resurgence properties of the
Hankel and Bessel functions of nearly equal order and argument,
Mathematische Annalen
363 (2015), no. 3, 1207-1263
-
The resurgence properties of the
incomplete gamma function I,
Analysis and Applications
14 (2016), no. 5, 631-677
-
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 large-argument asymptotic expansions of the Hankel and Bessel
functions,
Acta Applicandae Mathematicae 150 (2017), no. 1,
141-177
-
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 large-argument asymptotic expansions of the Lommel and allied
functions,
Studies in Applied Mathematics 140 (2018), no. 4, 508-541
-
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,
2144-2177
-
With A. B. Olde Daalhuis -
Asymptotic
expansions for the incomplete gamma function in the transition regions,
Mathematics of Computation 88 (2019), no. 318, 1805-1827
-
With A. B. Olde Daalhuis -
Large-parameter
asymptotic expansions for the Legendre and allied functions,
SIAM Journal on Mathematical Analysis 52 (2020), no. 1,
437-470
-
An extension of
Laplace's method,
Constructive Approximation
51 (2020), no. 2, 247-272
-
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 Schrödinger-type 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,
4328-4349
-
Dingle's final main rule, Berry's
transition, and Howls' conjecture, Journal of Physics A: Mathematical and Theoretical
55 (2022), no. 49, Article 494001, 25 pp.
-
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 153 (2023), no. 2, 417-440
-
Resurgence in the
transition region: The incomplete gamma function,
Symmetry, Integrability and Geometry: Methods and Applications
20
(2024), Article 026, 14 pp.
-
Simple error bounds for an
asymptotic expansion of the partition function,
The Ramanujan Journal 65 (2024), no. 4, 1757-1771
-
On the Borel
summability of formal solutions of certain higher-order linear ordinary
differential equations, Journal of Differential Equations
415 (2025), 645-700
-
With C. J. Howls, J. R. King, and A.
B. Olde Daalhuis -
Smoothing of the
higher-order Stokes phenomenon, submitted
-
Large-degree
asymptotic expansions for the Jacobi and allied functions, 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
|