Oberhettinger / Birnbaum / Lukacs Fourier Transforms of Distributions and Their Inverses

A Collection of Tables
1. Auflage 2014
ISBN: 978-1-4832-1902-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 180 Seiten, Web PDF

Fourier Transforms of Distributions and Their Inverses: A Collection of Tables is a collection of tables on the integrals of Fourier transforms of distributions and their inverses involving the class of functions which are nonnegative and integrable over the interval. The emphasis is on the probability densities, and a number of examples are provided. This book is organized into two parts and begins with an introduction to those properties of characteristic functions which are important in probability theory, followed by a description of the tables and their use. The first three tables contain Fourier transforms of absolutely continuous distribution functions, namely, even functions (including Legendre functions); functions vanishing identically for negative values of the argument (including arbitrary powers); and functions that do not belong to either of the above classes. The transform pairs are numbered consecutively and arranged systematically according to the analytical character of the frequency function. The next two tables give the inverse transforms of the functions listed in the first and third tables, respectively. This monograph will appeal to students and specialists in the fields of probability and mathematical statistics.

Autoren/Hrsg.

Oberhettinger, Fritz

Birnbaum, Z. W.

Lukacs, E.

Inhaltsverzeichnis

1;Front Cover;1
2;Fourier Transforms of Distributions and Their Inverses: A Collection of Tables;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;10
6;Introduction;14
6.1;Characteristic Functions;14
6.2;Description and Use of the Tables;18
6.3;Tables of the Appendix;25
6.4;References;25
7;PART I: TABLES OF FOURIER TRANSFORMS;26
7.1;TABLE I.
Even Functions;28
7.1.1;1. Algebraic Functions;30
7.1.2;2. Arbitrary Powers;33
7.1.3;3. Exponential Functions;36
7.1.4;4. Logarithmic Functions;40
7.1.5;5. Trigonometric Functions;43
7.1.6;6. Inverse Trigonometric Functions;49
7.1.7;7. Hyperbolic Functions;49
7.2;TABLE II.
Functions Vanishing Identically for Negative Values of the Argument;87
7.2.1;1. Algebraic Functions;88
7.2.2;2. Arbitrary Powers;90
7.2.3;3. Exponential Functions;92
7.2.4;4. Logarithmic Functions;95
7.2.5;5. Trigonometric Functions;97
7.2.6;6. Inverse Trigonometric Functions;99
7.2.7;7. Hyperbolic Functions;99
7.2.8;8. Gamma and Related Functions;102
7.2.9;9. Elliptic Integrals and Legendre Functions;103
7.2.10;10. Bessel Functions;104
7.2.11;11. Modified Bessel
Functions;106
7.2.12;12. Parabolic Cylindrical Functions;109
7.3;TABLE III.
Functions Not Belonging to Either of These Classes;110
8;PART II: TABLES OF THE INVERSE TRANSFORMS OF PART I;116
8.1;TABLE IA.
Even Functions;118
8.1.1;1. Algebraic Functions;119
8.1.2;2. Arbitrary Powers;119
8.1.3;3. Exponential Functions;120
8.1.4;4. Logarithmic Functions;121
8.1.5;5. Trigonometric Functions;122
8.1.6;6. Inverse Trigonometric Functions;123
8.1.7;7. Hyperbolic Functions;124
8.1.8;7a.Orthogonal Polynomials;128
8.1.9;8.Gamma Functions (Including Incomplete Gamma Functions) and Related Functions;129
8.1.10;9. Elliptic Integrals and Legendre Functions;138
8.1.11;10. Bessel Functions;145
8.1.12;11. Modified Bessel Functions;149
8.1.13;12. Functions Related to Bessel Functions;153
8.1.14;13. Parabolic Cylindrical Functions and Whittaker Functions;156
8.2;TABLE IIA.
Functions Vanishing Identically for Negative Values of the Argument;158
8.3;TABLE IIIA.
Functions Not Belonging to Either of These Classes;159
9;APPENDIX: DISTRIBUTION FUNCTIONS AND THEIR FOURIER TRANSFORMS FOUND IN THE STATISTICAL LITERATURE;164
9.1;TABLE A.
Univariate Density Functions;166
9.2;TABLE B.
Univariate Discrete Distributions;171
9.3;TABLE C.
Multivariate Density Functions;173
9.4;List of Abbreviations, Symbols, and Notations;175