Welcome to the home page of Gergő Nemes

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 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.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:

  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. 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

  31. An extension of Laplace's method,
    Constructive Approximation 51 (2020), no. 2, 247-272

  32. 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.

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

  34. 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

  35. 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

  36. 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