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The H-Function

Theory and Applications

  • A.M. Mathai
  • Ram Kishore Saxena
  • Hans J. Haubold

Table of contents

  1. Front Matter
    Pages i-xiv
  2. A. M. Mathai, Ram Kishore Saxena, Hans J. Haubold
    Pages 1-43
  3. A. M. Mathai, Ram Kishore Saxena, Hans J. Haubold
    Pages 45-74
  4. A. M. Mathai, Ram Kishore Saxena, Hans J. Haubold
    Pages 75-117
  5. A. M. Mathai, Ram Kishore Saxena, Hans J. Haubold
    Pages 119-138
  6. A. M. Mathai, Ram Kishore Saxena, Hans J. Haubold
    Pages 139-158
  7. A. M. Mathai, Ram Kishore Saxena, Hans J. Haubold
    Pages 159-203
  8. Back Matter
    Pages 205-268

About this book

Introduction

The topics of special H-function and fractional calculus are currently undergoing rapid changes both in theory and application. Taking into account the latest research results, the authors delve into these topics as they relate to applications to problems in statistics, physics, and engineering, particularly in condensed matter physics, plasma physics, and astrophysics.

The book sets forth the definitions, contours, existence conditions, and particular cases for the H-function, then explores the properties and relationships among the Laplace, Fourier, Hankel, and other transforms. From here, the H-functions are utilized for applications in statistical distribution theory, structures of random variables, generalized distributions, Mathai’s pathway models, and versatile integrals. Functions of matrix argument are introduced with a focus on real-valued scalar functions when the matrices are real or Hermitian positive-definite. The text concludes with important recent applications to physical problems in reaction, diffusion, reaction-diffusion theory and statistics, and superstatistics. Generalized entropies as well as applications in astrophysics are dealt with.

Over the last few years, material in this book has been added to various courses and developed to meet the needs of scholars at the PhD level. All exercises in the book have been used to probe the knowledge and ability of mathematics, statistics, and physics to students and researchers. 

Keywords

Diffusion Disordered systems Dynamical systems theory Fractional calculus Mathai pathway models Reaction diffusion applied mathematics Stochastic theory applications H-functions applied mathematics astrophysics condensed matter distribution operator statistical distribution applications

Authors and affiliations

  • A.M. Mathai
    • 1
  • Ram Kishore Saxena
    • 2
  • Hans J. Haubold
    • 3
  1. 1.Centre for Mathematical Sciences (CMS)Arunapuram P.O., PalaIndia
  2. 2.JodhpurIndia
  3. 3.Vienna International CentreUnited NationsWienAustria

Bibliographic information