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

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Complex Differential and Difference Equations

Proceedings of the School and Conference held at Będlewo, Poland, September 2-15, 2018

Edited by: , , , and

Language: English

Published/Copyright: 2020

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De Gruyter Proceedings in Mathematics

About this book

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.

Author / Editor information

G. Filipuk, S. Michalik, and H. Żołądek, Warsaw, Poland; A. Lastra, Alcalá, Spain; G. Łysik, Kielce, Poland; Y. Takei, Kyoto, Japan.

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Frontmatter
I

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Preface
V

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Contents
IX

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Part I
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Group-theoretical origin of symmetries of hypergeometric class equations and functions
3
J. Dereziński

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The algebro-geometric solution method for algebraic differential equations – an introduction by examples
129
J. Rafael Sendra and Franz Winkler

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Movable singularity of some Hamiltonian systems
147
Masafumi Yoshino

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Some aspects of summability
171
Jorge Mozo Fernández

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Convolution product and resurgence
219
Shingo Kamimoto

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Part II
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The relation between the Bessel function and the Borel sum of the WKB solution
245
Toshinori Takahashi and Mika Tanda

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A relation between the exact WKB analysis and the topological recursion – in the case of the Gauss hypergeometric differential equation
259
Yumiko Takei

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On the solutions of the Airy equation and their zeros
267
Federico Zullo

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Intersection theory for Euler integral representations of GKZ hypergeometric functions: Appell’s F₁ case
283
Saiei-Jaeyeong Matsubara-Heo

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Ultradiscrete limit of the spectral polynomial of the q-Heun equation
297
Kentaro Kojima, Tsukasa Sato and Kouichi Takemura

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Isomonodromy deformations with coalescing eigenvalues and applications – Będlewo 2018
313
Davide Guzzetti

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Potential vector fields and isomonodromic tau functions in terms of flat coordinates
327
Toshiyuki Mano

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Solutions to the extended WDVV equations and the Painlevé VI equation
343
Mitsuo Kato, Toshiyuki Mano and Jiro Sekiguchi

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On the instanton-type expansions for Painlevé transcendents and elliptic functions
365
Yoshitsugu Takei

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Formal solutions to ordinary differential equation via dimensioned numbers
379
Hideaki Izumi

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Gevrey estimates for certain moment partial differential equations
391
Sławomir Michalik and Maria Suwińska

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A Nagumo-type theorem for a class of singular nonlinear equations
409
Mark Philip F. Ona and Jose Ernie C. Lope

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The Stokes phenomenon of the Cauchy problem for certain partial differential equations with variable coefficients depending on the time variable
419
Bożena Tkacz

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Some notes on the parametric Borel summability for linear singularly perturbed Cauchy problems with linear fractional transforms
435
Alberto Lastra and Stéphane Malek

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On k-summability of formal solutions to the Cauchy problems for some linear q-difference-differential equations
447
Kunio Ichinobe and Shunya Adachi

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Publishing information

Pages and Images/Illustrations in book

eBook published on:

November 18, 2019

eBook ISBN:

9783110611427

Hardcover published on:

November 18, 2019

Hardcover ISBN:

9783110609523

Pages and Images/Illustrations in book

Front matter:

10

Main content:

463

Illustrations:

10

Coloured Illustrations:

7

Tables:

15

https://doi.org/10.1515/9783110611427

eBook ISBN: 9783110611427

Hardcover ISBN: 9783110609523

Keywords for this book

Algebraische Differentialgleichung; Funktionentheorie; Komplexe Differentialgleichung; Reihenlösung; WKB-Methode

Audience(s) for this book

Researchers and graduate students in complex analysis, differential equations, and applications.

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Manufacturer information:: Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin; productsafety@degruyterbrill.com

Complex Differential and Difference Equations

Overview

About this book

Author / Editor information

Topics

Table of contents

Frontmatter

Preface

Contents

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

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

Bibliographic data

Intersection theory for Euler integral representations of GKZ hypergeometric functions: Appell’s F₁ case