The H-Function: Theory and Applications

ISBN-13: 9781489984586 / Angielski / Miękka / 2014 / 268 str.

Professor of Mathematics and Statistics;Ram Kishore Saxena;Hans J Haubold

Opis

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.

Recenzje

From the reviews:

"The book is devoted to the study of properties of Fox's H-function and to the description of modern applications of this function. ... also contains an extended Bibliography on the subject, a Glossary of Symbols, and Indexes. ... combines the features of a research monograph, a table of special functions, as well as of a textbook for those who intend to apply the properties of the H-function in their research." (Sergei V. Rogosin, Zentralblatt MATH, Vol. 1181, 2010)

"It is fairly comprehensive, competently researched, and as thoroughly up-to-date as a book can be, as well as being well organized, very well and very clearly written, authoritative and useful. ... easily accessible to a beginner in the field as well as extremely valuable reference source for those who know the matter well. ... It is an ideal book for those wishing to start research in this area and it can be used readily as a textbook in a one-semester graduate course on H-functions." (Djurdje Cvijovic, Mathematical Reviews, Issue 2011 j)

Spis treści

On the H-Function With Applications.- H-Function in Science and Engineering.- Fractional Calculus.- Applications in Statistics.- Functions of Matrix Argument.- Applications in Astrophysics Problems.

Blurb

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.