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

The H-Function (eBook, PDF)

Theory and Applications

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer-Verlag GmbH
• Seitenzahl: 268
• Erscheinungstermin: 10. Oktober 2009
• Englisch
• ISBN-13: 9781441909169
• Artikelnr.: 37362657

Inhaltsangabe

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.

Rezensionen

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)