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.
