Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences
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348 IIIIIIII
IIIII
A. M. Mathai R. K. Saxena McGill University, Montreal/Canada
Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences
Springer-Verlag Berlin-Heidelberg • New York 1973
IIIIIIIIIIII
A M S Subject Classifications (1970): Primary: 33-02, 3 3 A 3 0 , 3 3 A 3 5 Secondary: 62E15, 6 2 H 1 0 , 8 0 A 2 0 , 9 4 A 0 5
I S B N 3-540-06482-6 S p r i n g e r - V e r l a g Berlin • H e i d e l b e r g • N e w Y o r k I S B N 0-387-06482-6 S p r i n g e r - V e r l a g N e w Y o r k • H e i d e l b e r g • Berlin
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin • Heidelberg i973. Library of Congress Catalog Card Number 73-I3489. Printed in Germany. Offsetdruck: Julius Beltz, Hemsbaci~Bergstr.
PREFACE
This book deals with generalized hypergeometric functions. The main topic is Meijer's G-function and its applications to various practical problems in Statistical Distributions, Prior and Posterior Distributions, Characterizations of Probability Laws. Hard Limiting of Several Sinusoidal Signals in Communication Theory, Conduction of Heat and Cooling and Dual integral Equations. This book gives a balanced treatment of theory and applications. Out of the seven chapters the last three are devoted to applications. This book can be used as a text or as a reference book. SPECIAL FEATURES: (i)
Most of the materials in Chapter 3 and all the materials in the Chapters 4 to 7 are based on recent publications and thus they are not available in any of the books in this field.
(2)
Each chapter contains a list of exercises and most of these problems are from recent research papers.
(3)
This is the first book in which the logarithmic cases and computable representations of Meijer's G-function are discussed in detail. Chapter 5 deals with computable representations of hypergeometric and G-functions in the most general logarithmic cases.
(4)
This is the first book in which applications of Meijer's G-function in a number of topics in Statistics, Communication Theory and Theoretical Physics, are given. These results are from papers published in 1970,1971,1972 and papers to appear in 1972-73.
(5)
This is the first book in which hypergeometric functions with matrix arguments, together with their application to statistical problems are discussed. These generalized functions are defined in terms of Zonal Polynomials of real symmetric matrices.
(6)
On each topic the key formulas, together with the outlines of the proofs, are given in the text. From these key formulas all the results available on elementary Special Functions, which are
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