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This text begins with definitions, contours, existence conditions and particular cases of the H-function. It then explores various H-function applications such as in statistical distribution theory, generalized distributions, Mathai's pathway models and more.
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.
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.
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)
"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)