Skip to main content
SpringerLink
Log in
SpringerLink
Log in

Global Analysis in Linear Differential Equations

  • Book
  • © 1999

Overview

Authors:
  1. Mitsuhiko Kohno

    1. Department of Mathematics, Kumamoto University, Kumamoto, Japan

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Mathematics and Its Applications (MAIA, volume 471)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (7 chapters)

  1. Front Matter

    Pages i-xvi
    Download chapter PDF

  2. Preparations

    • Mitsuhiko Kohno
    Pages 1-160

  3. Gauss and Airy Equations

    • Mitsuhiko Kohno
    Pages 161-218

  4. Linear Differential Equations

    • Mitsuhiko Kohno
    Pages 219-289

  5. Reduction Problems

    • Mitsuhiko Kohno
    Pages 291-335

  6. Monodromy Groups for Hypergeometric Systems

    • Mitsuhiko Kohno
    Pages 337-376

  7. Connection Problem for Hypergeometric Systems

    • Mitsuhiko Kohno
    Pages 377-445

  8. Stokes Phenomenon

    • Mitsuhiko Kohno
    Pages 447-513

  9. Back Matter

    Pages 515-528
    Download chapter PDF
Back to top

Keywords

About this book

Since the initiative works for global analysis of linear differential equations by G.G. Stokes and B. Riemann in 1857, the Airy function and the Gauss hypergeometric function became the most important and the greatest practical special functions, which have a variety of applications to mathematical science, physics and engineering. The cffcctivity of these functions is essentially due to their "behavior in the large" . For instance, the Airy function plays a basic role in the asymptotic analysis of many functions arising as solutions of differential equations in several problems of applied math­ ematics. In case of the employment of its behavior, one should always pay attention to the Stokes phenomenon. On the other hand, as is well-known, the Gauss hypergeometric function arises in all fields of mathematics, e.g., in number theory, in the theory of groups and in analysis itself. It is not too much to say that all power series are special or extended cases of the hypergeometric series. For the full use of its properties, one needs connection formulas or contiguous relations.

Authors and Affiliations

  • Department of Mathematics, Kumamoto University, Kumamoto, Japan

    Mitsuhiko Kohno

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation