Complex Differential and Difference Equations : : Proceedings of the School and Conference held at Będlewo, Poland, September 2-15, 2018 / / ed. by Galina Filipuk, Alberto Lastra, Sławomir Michalik, Yoshitsugu Takei, Henryk Żołądek.

• Superior document: Title is part of eBook package: De Gruyter DG Ebook Package English 2020
• MitwirkendeR: Adachi, Shunya,; Dereziński, J.,; Fernández, Jorge Mozo,; Guzzetti, Davide,; Ichinobe, Kunio,; Izumi, Hideaki,; Kamimoto, Shingo,; Kato, Mitsuo,; Kojima, Kentaro,; Lastra, Alberto,; Lope, Jose Ernie C.,; Malek, Stéphane,; Mano, Toshiyuki,; Matsubara-Heo, Saiei-Jaeyeong,; Michalik, Sławomir,; Ona, Mark Philip F.,; Sato, Tsukasa,; Sekiguchi, Jiro,; Sendra, J. Rafael,; Suwińska, Maria,; Takahashi, Toshinori,; Takei, Yoshitsugu,; Takei, Yumiko,; Takemura, Kouichi,; Tanda, Mika,; Tkacz, Bożena,; Winkler, Franz,; Yoshino, Masafumi,; Zullo, Federico,
• HerausgeberIn: Filipuk, Galina,; Lastra, Alberto,; Michalik, Sławomir,; Takei, Yoshitsugu,; Żołądek, Henryk,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2019]; ©2020
• Year of Publication: 2019
• Language: English
• Series: De Gruyter Proceedings in Mathematics
• Physical Description: 1 online resource (X, 463 p.)

With a balanced combination of longer survey articles and shorter, peer-reviewed research-level presentations on the topic of differential and difference equations on the complex domain, this edited volume presents an up-to-date overview of areas such as WKB analysis, summability, resurgence, formal...

Table of Contents

• Frontmatter
• Preface
• Contents
• Part I
• Group-theoretical origin of symmetries of hypergeometric class equations and functions
• The algebro-geometric solution method for algebraic differential equations – an introduction by examples
• Movable singularity of some Hamiltonian systems
• Some aspects of summability
• Convolution product and resurgence
• Part II
• The relation between the Bessel function and the Borel sum of the WKB solution
• A relation between the exact WKB analysis and the topological recursion – in the case of the Gauss hypergeometric differential equation
• On the solutions of the Airy equation and their zeros
• Intersection theory for Euler integral representations of GKZ hypergeometric functions: Appell’s F1 case
• Ultradiscrete limit of the spectral polynomial of the q-Heun equation
• Isomonodromy deformations with coalescing eigenvalues and applications – Będlewo 2018
• Potential vector fields and isomonodromic tau functions in terms of flat coordinates
• Solutions to the extended WDVV equations and the Painlevé VI equation
• On the instanton-type expansions for Painlevé transcendents and elliptic functions
• Formal solutions to ordinary differential equation via dimensioned numbers
• Gevrey estimates for certain moment partial differential equations
• A Nagumo-type theorem for a class of singular nonlinear equations
• The Stokes phenomenon of the Cauchy problem for certain partial differential equations with variable coefficients depending on the time variable
• Some notes on the parametric Borel summability for linear singularly perturbed Cauchy problems with linear fractional transforms
• On k-summability of formal solutions to the Cauchy problems for some linear q-difference-differential equations