from bessel to multi index mittagcleffler functions

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Elementary Introduction To The Theory Of Pseudodifferential Operators

Author : Xavier Saint Raymond
ISBN : 9781351452922
Genre : Mathematics
File Size : 67. 65 MB
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In the 19th century, the Fourier transformation was introduced to study various problems of partial differential equations. Since 1960, this old tool has been developed into a well-organized theory called microlocal analysis that is based on the concept of the pseudo-differential operator. This book provides the fundamental knowledge non-specialists need in order to use microlocal analysis. It is strictly mathematical in the sense that it contains precise definitions, statements of theorems and complete proofs, and follows the usual method of pure mathematics. The book explains the origin of the theory (i.e., Fourier transformation), presents an elementary construcion of distribution theory, and features a careful exposition of standard pseudodifferential theory. Exercises, historical notes, and bibliographical references are included to round out this essential book for mathematics students; engineers, physicists, and mathematicians who use partial differential equations; and advanced mathematics instructors.

Table Of Integrals Series And Products

Author : I. S. Gradshteyn
ISBN : 9781483265643
Genre : Mathematics
File Size : 86. 10 MB
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Table of Integrals, Series, and Products provides information pertinent to the fundamental aspects of integrals, series, and products. This book provides a comprehensive table of integrals. Organized into 17 chapters, this book begins with an overview of elementary functions and discusses the power of binomials, the exponential function, the logarithm, the hyperbolic function, and the inverse trigonometric function. This text then presents some basic results on vector operators and coordinate systems that are likely to be useful during the formulation of many problems. Other chapters consider inequalities that range from basic algebraic and functional inequalities to integral inequalities and fundamental oscillation and comparison theorems for ordinary differential equations. This book discusses as well the important part played by integral transforms. The final chapter deals with Fourier and Laplace transforms that provides so much information about other integrals. This book is a valuable resource for mathematicians, engineers, scientists, and research workers.

A Treatise On The Theory Of Bessel Functions

Author : G. N. Watson
ISBN : 0521483913
Genre : Mathematics
File Size : 36. 53 MB
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This monumental 1995 treatise by the late Professor G. N. Watson wil be indispensable to mathematicians and physicists.

Number Theory

Author : Henri Cohen
ISBN : 9780387498942
Genre : Mathematics
File Size : 36. 52 MB
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This book deals with several aspects of what is now called "explicit number theory." The central theme is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The local aspect, global aspect, and the third aspect is the theory of zeta and L-functions. This last aspect can be considered as a unifying theme for the whole subject.

Integral Transforms And Their Applications

Author : B. Davies
ISBN : 9781489926913
Genre : Mathematics
File Size : 63. 46 MB
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In preparing this second edition I have restricted myself to making small corrections and changes to the first edition. Two chapters have had extensive changes made. First, the material of Sections 14.1 and 14.2 has been rewritten to make explicit reference to the book of Bleistein and Handelsman, which appeared after the original Chapter 14 had been written. Second, Chapter 21, on numerical methods, has been rewritten to take account of comparative work which was done by the author and Brian Martin, and published as a review paper. The material for all of these chapters was in fact, prepared for a transla tion of the book. Considerable thought has been given to a much more com prehensive revision and expansion of the book. In particular, there have been spectacular advances in the solution of some non-linear problems using isospectra1 methods, which may be re garded as a generalization of the Fourier transform. However, the subject is a large one, and even a modest introduction would have added substantially to the book. Moreover, the recent book by Dodd et al. is at a similar level to the present volume. Similarly, I have refrained from expanding the chapter on num erical methods into a complete new part of the book, since a specialized monograph on numerical methods is in preparation in collaboration with a colleague.

Handbook Of Mathematical Functions

Author : Milton Abramowitz
ISBN : 9780486158242
Genre : Mathematics
File Size : 58. 64 MB
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A classic resource for working with special functions, standard trig, and exponential logarithmic definitions and extensions, it features 29 sets of tables, some to as high as 20 places.

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