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 solutions, integrability, and several algebraic aspects of differential and difference equations.

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