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| Author | : A. M. Mathai |
| Publisher | : Springer |
| Total Pages | : 322 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540378006 |
| Author | : A. M. Mathai |
| Publisher | : |
| Total Pages | : 328 |
| Release | : 2014-01-15 |
| Genre | : |
| ISBN | : 9783662166468 |
| Author | : Lucy Joan Slater |
| Publisher | : Cambridge University Press |
| Total Pages | : 0 |
| Release | : 1966-01-02 |
| Genre | : Mathematics |
| ISBN | : 052106483X |
The theory of generalized hypergeometric functions is fundamental in the field of mathematical physics, since all the commonly used functions of analysis (Besse] Functions, Legendre Functions, etc.) are special cases of the general functions. The unified theory provides a means for the analysis of the simpler functions and can be used to solve the more complicated equations in physics. The generalized Gauss function is also used in mathematical statistics and the basic analogues of the Gauss functions have applications in the field of number theory. Dr Slater's treatment leads on from a discussion of the Gauss functions to the basic hypergeometric functions, the hypergeometric integrals, bilateral series and Appel series. This book was planned jointly with the late Professor W. N. Bailey as an extended revision of his Cambridge Mathematical Tract (1935) on the subject and Dr Slater has continued it single-handed since Professor Bailey's death, incorporating in it the results of many of her own researches.
| Author | : A.M. Mathai |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 480 |
| Release | : 2008-02-13 |
| Genre | : Science |
| ISBN | : 0387758941 |
This book, written by a highly distinguished author, provides the required mathematical tools for researchers active in the physical sciences. The book presents a full suit of elementary functions for scholars at PhD level. The opening chapter introduces elementary classical special functions. The final chapter is devoted to the discussion of functions of matrix argument in the real case. The text and exercises have been class-tested over five different years.
| Author | : A. M. Mathai |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 264 |
| Release | : 1993 |
| Genre | : Mathematics |
| ISBN | : |
Complicated generalized special functions such as Meijer's G-functions and functions of matrix arguments are here presented at a level suitable for every potential user. This handbook is thus a valuable reference source and a manual for researchers and advanced students in mathematical statistics, mathematical physics, several branches of mathematics, engineering problems, econometrics, and various applied areas where transcendental functions are used.
| Author | : K Srinivasa Rao |
| Publisher | : Iph001 |
| Total Pages | : 200 |
| Release | : 2018-10-24 |
| Genre | : Science |
| ISBN | : 9780750314947 |
The aims and objectives of this book are to present a unified approach to the study of special functions of mathematics, which are ubiquitous and essential to a formulation of any physical or engineering problem in a mathematical format. In this detailed monograph, the second order Ordinary Differential Equation of Carl Friedrich Gauss is the starting point for the study of special functions. This is a simple, unified and novel approach to the treatment of the subject. The new feature in this presentation is that of the group theory associated with special functions. Generalized Hypergeometric Functions: Transformations and group theoretical aspects outlines the important relationship between the Gauss hypergeometric equation and corresponding special functions. Each chapter details the application of group theory to the study of special functions and discusses various transformations, group theory, and their relevance In various applications. It is a relatively self-contained book that includes extensive introductory expositions of group theory. Offering an original approach to the hypergeometric equation and related function, this book is important for fundamental understanding of the mathematics underlying various aspects of physics, applied mathematics, and engineering. With the use of worked examples, proofs, summaries and references, this work can be used in various courses of study and research, and it is also useful for self-study. Book jacket.
| Author | : James B. Seaborn |
| Publisher | : |
| Total Pages | : 250 |
| Release | : 1991-01-01 |
| Genre | : Fonctions hypergéométriques |
| ISBN | : 9783540975588 |
Many of the special functions of applied mathematics can be expressed in terms of hypergeometric functions. In this book each special function is seen to arise in one or more physical contexts as a solution of a differential equation that can be transformed into a hypergeometric equation. The special function is then defined in terms of a generalized hypergeometric function and the equivalence to alternate definitions is established. Many of the interesting and important properties of the special functions that one encounters in standard upper level textbooks on engineering, they physical sciences, and other branches of applied mathematics are derived. The close connection of the development with applications is emphasized throughout the book in the text and in the exercises.
| Author | : A.M. Mathai |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 276 |
| Release | : 2009-10-10 |
| Genre | : Science |
| ISBN | : 1441909168 |
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.
| Author | : Rudolf Gorenflo |
| Publisher | : Springer Nature |
| Total Pages | : 548 |
| Release | : 2020-10-27 |
| Genre | : Science |
| ISBN | : 3662615509 |
The 2nd edition of this book is essentially an extended version of the 1st and provides a very sound overview of the most important special functions of Fractional Calculus. It has been updated with material from many recent papers and includes several surveys of important results known before the publication of the 1st edition, but not covered there. As a result of researchers’ and scientists’ increasing interest in pure as well as applied mathematics in non-conventional models, particularly those using fractional calculus, Mittag-Leffler functions have caught the interest of the scientific community. Focusing on the theory of Mittag-Leffler functions, this volume offers a self-contained, comprehensive treatment, ranging from rather elementary matters to the latest research results. In addition to the theory the authors devote some sections of the work to applications, treating various situations and processes in viscoelasticity, physics, hydrodynamics, diffusion and wave phenomena, as well as stochastics. In particular, the Mittag-Leffler functions make it possible to describe phenomena in processes that progress or decay too slowly to be represented by classical functions like the exponential function and related special functions. The book is intended for a broad audience, comprising graduate students, university instructors and scientists in the field of pure and applied mathematics, as well as researchers in applied sciences like mathematical physics, theoretical chemistry, bio-mathematics, control theory and several other related areas.
| Author | : Themistocles M. Rassias |
| Publisher | : Springer Nature |
| Total Pages | : 694 |
| Release | : 2019-12-12 |
| Genre | : Mathematics |
| ISBN | : 3030313395 |
An international community of experts scientists comprise the research and survey contributions in this volume which covers a broad spectrum of areas in which analysis plays a central role. Contributions discuss theory and problems in real and complex analysis, functional analysis, approximation theory, operator theory, analytic inequalities, the Radon transform, nonlinear analysis, and various applications of interdisciplinary research; some are also devoted to specific applications such as the three-body problem, finite element analysis in fluid mechanics, algorithms for difference of monotone operators, a vibrational approach to a financial problem, and more. This volume is useful to graduate students and researchers working in mathematics, physics, engineering, and economics.
