Complex Differential and Difference Equations : Proceedings of the School and Conference Held at Będlewo, Poland, September 2-15, 2018

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. * A collection of select articles in complex differential and difference equations * Documents the presentations of an international school and conference * Covers topics such as WKB analysis, summability, formal solutions, integrability, etc. 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 F 1 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 The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications