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.

lgrsnf/F:\Library.nu\5c\_122431.5c4c082a3c657af784b124a92bc5b6cf.pdf

nexusstc/The H-Function/5c4c082a3c657af784b124a92bc5b6cf.pdf

scihub/10.1007/978-1-4419-0916-9.pdf

zlib/Science (General)/A.M. Mathai, Ram Kishore Saxena, Hans J. Haubold (auth.)/The H-Function: Theory and Applications_860666.pdf

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

by A.M. Mathai, Ram Kishore Saxena, Hans J. Haubold

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

A M Mathai; Ram Kishore Saxena; Hans J Haubold

Springer US

United States, United States of America

New York, NY, New York State, 2009

Springer Nature, New York, 2010

New York, NY, cop. 2010

Dordrecht, 2009

2010, 2009

до 2011-01

lg542549

{"edition":"1","isbns":["144190915X","1441909168","9781441909152","9781441909169"],"last_page":268,"publisher":"Springer New York"}

MiU

TheH-function or popularly known in the literature as Fox’sH-function has recently found applications in a large variety of problems connected with reaction, diffusion, reaction–diffusion, engineering and communication, fractional differ- tial and integral equations, many areas of theoretical physics, statistical distribution theory, etc. One of the standard books and most cited book on the topic is the 1978 book of Mathai and Saxena. Since then, the subject has grown a lot, mainly in the elds of applications. Due to popular demand, the authors were requested to - grade and bring out a revised edition of the 1978 book. It was decided to bring out a new book, mostly dealing with recent applications in statistical distributions, pa- way models, nonextensive statistical mechanics, astrophysics problems, fractional calculus, etc. and to make use of the expertise of Hans J. Haubold in astrophysics area also. It was decided to con ne the discussion toH-function of one scalar variable only. Matrix variable cases and many variable cases are not discussed in detail, but an insight into these areas is given. When going from one variable to many variables, there is nothing called a unique bivariate or multivariate analogue of a givenfunction. Whatever be the criteria used, there may be manydifferentfunctions quali ed to be bivariate or multivariate analogues of a given univariate function. Some of the bivariate and multivariateH-functions, currently in the literature, are also questioned by many authors.
Erscheinungsdatum: 30.10.2009

The two main topics emphasized in this book, special functions and fractional calculus, are currently under fast development in theory and application to many problems in statistics, physics, and engineering, particularly in condensed matter physics, plasma physics, and astrophysics. The book begins by setting forth definitions, contours, existence conditions, and particular cases of the H-function. The authors then deal with Laplace, Fourier, Hankel, and other transforms. As these relations are explored, fractional calculus and its relations to H-functions emerge with important results on fra

Front Matter....Pages i-xiv
On the H -Function With Applications....Pages 1-43
H -Function in Science and Engineering....Pages 45-74
Fractional Calculus....Pages 75-117
Applications in Statistics....Pages 119-138
Functions of Matrix Argument....Pages 139-158
Applications in Astrophysics Problems....Pages 159-203
Back Matter....Pages 205-268

2011-06-04