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Special Functions of Mathematical (Geo-)Physics

  • Willi Freeden
  • Martin Gutting

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Willi Freeden, Martin Gutting
    Pages 1-21
  3. Auxiliary Functions

    1. Front Matter
      Pages 23-23
    2. Willi Freeden, Martin Gutting
      Pages 25-46
    3. Willi Freeden, Martin Gutting
      Pages 47-109
  4. Spherically Oriented Functions

    1. Front Matter
      Pages 111-111
    2. Willi Freeden, Martin Gutting
      Pages 113-210
    3. Willi Freeden, Martin Gutting
      Pages 211-283
    4. Willi Freeden, Martin Gutting
      Pages 285-345
    5. Willi Freeden, Martin Gutting
      Pages 347-361
    6. Willi Freeden, Martin Gutting
      Pages 363-391
  5. Periodically Oriented Functions

    1. Front Matter
      Pages 393-393
    2. Willi Freeden, Martin Gutting
      Pages 395-425
    3. Willi Freeden, Martin Gutting
      Pages 427-482
    4. Willi Freeden, Martin Gutting
      Pages 483-484
  6. Back Matter
    Pages 485-501

About this book

Introduction

Special functions enable us to formulate a scientific problem by reduction such that a new, more concrete problem can be attacked within a well-structured framework, usually in the context of differential equations. A good understanding of special functions provides the capacity to recognize the causality between the abstractness of the mathematical concept and both the impact on and cross-sectional importance to the scientific reality.

The special functions to be discussed in this monograph vary greatly, depending on the measurement parameters examined (gravitation, electric and magnetic fields, deformation, climate observables, fluid flow, etc.) and on the respective field characteristic (potential field, diffusion field, wave field). The differential equation under consideration determines the type of special functions that are needed in the desired reduction process.

Each chapter closes with exercises that reflect significant topics, mostly in computational applications. As a result, readers are not only directly confronted with the specific contents of each chapter, but also with additional knowledge on mathematical fields of research, where special functions are essential to application. All in all, the book is an equally valuable resource for education in geomathematics and the study of applied and harmonic analysis.

Students who wish to continue with further studies should consult the literature given as supplements for each topic covered in the exercises.

Keywords

Cauchy–Navier and Navier-Stokes equation Laplace and Poisson equation Maxwell equation constructive approximation by function systems spherically and periodically oriented functions spheroidization and periodization

Authors and affiliations

  • Willi Freeden
    • 1
  • Martin Gutting
    • 2
  1. 1., Geomathematics GroupUniversity of KaiserslauternKaiserslauternGermany
  2. 2., Geomathematics GroupUniversity of KaiserslauternKaiserslauternGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-0563-6
  • Copyright Information Springer Basel 2013
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0348-0562-9
  • Online ISBN 978-3-0348-0563-6
  • Series Print ISSN 2296-5009
  • Series Online ISSN 2296-5017
  • Buy this book on publisher's site
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