The H-Function: Theory and Applications / Edition 1

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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 fractional differentiation and fractional integral operators.

The latter chapters explore applications of H-functions in statistical distribution theory, structures of random variables, generalized distributions, Mathai's pathway models, and versatile integrals. The authors also present an introduction to functions of matrix argument, with special focus on the space of Hermitian positive matrices. The book concludes with the most recent applications of H-functions and fractional calculus to physical problems in reactions, diffusion, reaction-diffusion theory, statistics, superstatistics, and generalized entropies.

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Editorial Reviews

From the Publisher

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 Cvijović, Mathematical Reviews, Issue 2011 j)

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Product Details

  • ISBN-13: 9781441909152
  • Publisher: Springer New York
  • Publication date: 10/30/2009
  • Edition description: 2010
  • Edition number: 1
  • Pages: 268
  • Product dimensions: 6.40 (w) x 9.30 (h) x 0.90 (d)

Table of Contents

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.

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