Welcome to the home page of Gergő Nemes

Gergő Nemes is a postdoctoral research fellow
at the Alfréd Rényi Institute of Mathematics of the
Hungarian Academy of Sciences.
He has a Ph.D. degree in Mathematics.

Address:

Alfréd Rényi Institute of Mathematics
Hungarian Academy of Sciences
Reáltanoda utca 13-15
H-1053, 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 e-mail at nemes.gergo@renyi.mta.hu.


Research interests:

        Asymptotic Analysis

        Écalle Theory

        Exact WKB Analysis

        Special Functions


Publications:

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

  2. New asymptotic expansion for the Gamma function,
    Archiv der Mathematik
    95 (2010), no. 2, 161-169

  3. Asymptotic expansion for log n! in terms of the reciprocal of a triangular number,
    Acta Mathematica Hungarica
    129 (2010), no. 3, 254-262

  4. More accurate approximations for the Gamma function,
    Thai Journal of Mathematics 9 (2011), no. 1, 21-28

  5. On the coefficients of an asymptotic expansion related to Somos' Quadratic Recurrence Constant,
    Applicable Analysis and Discrete Mathematics
    5 (2011)
    , no. 1, 60-66

  6. 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.

  7. With A. Nemes - A note on the Landau constants,
    Applied Mathematics and Computation 217 (2011), no. 21, 8543-8546

  8. Proofs of two conjectures on the Landau constants,
    Journal of Mathematical Analysis and Applications 388 (2012), no. 2, 838-844

  9. 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

  10. A remark on some accurate estimates of p,
    Journal of Mathematical Inequalities 6 (2012), no. 4, 517-521

  11. A solution to an open problem on Mathieu series posed by Hoorfar and Qi,
    Acta Mathematica Vietnamica 37 (2012), no. 3, 301-310

  12. 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

  13. Generalization of Binet's Gamma function formulas,
    Integral Transforms and Special Functions 24 (2013), no. 8, 597-606

  14. An explicit formula for the coefficients in Laplace's method,
    Constructive Approximation 38 (2013), no. 3, 471-487

  15. The resurgence properties of the large-order asymptotics of the Hankel and Bessel functions,
    Analysis and Applications 12 (2014), no. 4, 403-462

  16. The resurgence properties of the large order asymptotics of the Anger-Weber function I,
    Journal of Classical Analysis 4 (2014), no. 1, 1-39

  17. The resurgence properties of the large order asymptotics of the Anger-Weber function II,
    Journal of Classical Analysis 4 (2014), no. 2, 121-147

  18. 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.

  19. On the large argument asymptotics of the Lommel function via Stieltjes transforms,
    Asymptotic Analysis 91 (2015), no. 3-4, 265-281

  20. 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

  21. The resurgence properties of the incomplete gamma function II,
    Studies in Applied Mathematics 135 (2015), no. 1, 86-116

  22. The resurgence properties of the Hankel and Bessel functions of nearly equal order and argument,
    Mathematische Annalen
    363 (2015), no. 3, 1207-1263

  23. The resurgence properties of the incomplete gamma function I,
    Analysis and Applications 14 (2016), no. 5, 631-677

  24. 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.

  25. Error bounds for the large-argument asymptotic expansions of the Hankel and Bessel functions,
    Acta Applicandae Mathematicae
    150 (2017), no. 1, 141-177

  26. 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.

  27. Error bounds for the large-argument asymptotic expansions of the Lommel and allied functions,
    Studies in Applied Mathematics 140 (2018), no. 4, 508-541

  28. 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

  29. 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

  30. An extension of Laplace's method,
    Constructive Approximation, online first

  31. With A. B. Olde Daalhuis - Large-parameter asymptotic expansions for the Legendre 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