Fourier Transforms of Distributions and Their Inverses - 1st Edition - ISBN: 9780125236508, 9781483219028

Fourier Transforms of Distributions and Their Inverses

1st Edition

A Collection of Tables

Authors: Fritz Oberhettinger
Editors: Z. W. Birnbaum E. Lukacs
eBook ISBN: 9781483219028
Imprint: Academic Press
Published Date: 28th September 1973
Page Count: 180
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Description

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.

Table of Contents


Preface

Introduction

Characteristic Functions

Description and Use of the Tables

Tables of the Appendix

References

Part I. Tables of Fourier Transforms

Table I. Even Functions

1. Algebraic Functions

2. Arbitrary Powers

3. Exponential Functions

4. Logarithmic Functions

5. Trigonometric Functions

6. Inverse Trigonometric Functions

7. Hyperbolic Functions

8. Gamma Functions (Including Incomplete Gamma Functions) and Related Functions

9. Elliptic Integrals and Legendre Functions

10. Bessel Functions

11. Modified Bessel Functions

12. Functions Related to Bessel Functions

13. Parabolic Cylindrical Functions

Table II. Functions Vanishing Identically for Negative Values of the Argument

1. Algebraic Functions

2. Arbitrary Powers

3. Exponential Functions

4. Logarithmic Functions

5. Trigonometric Functions

6. Inverse Trigonometric Functions

7. Hyperbolic Functions

8. Gamma and Related Functions

9. Elliptic Integrals and Legendre Functions

10. Bessel Functions

11. Modified Bessel Functions

12. Parabolic Cylindrical Functions

Table III. Functions Not Belonging to Either of These Classes

Part II. Tables of the Inverse Transforms of Part I

Table IΑ· Even Functions

1. Algebraic Functions

2. Arbitrary Powers

3. Exponential Functions

4. Logarithmic Functions

5. Trigonometric Functions

6. Inverse Trigonometric Functions

7. Hyperbolic Functions

7a. Orthogonal Polynomials

8. Gamma Functions (Including Incomplete Gamma Functions) and Related Functions

9. Elliptic Integrals and Legendre Functions

10. Bessel Functions

11. Modified Bessel Functions

12. Functions Related to Bessel Functions

13. Parabolic Cylindrical Functions and Whittaker Functions

Table IIA. Functions Vanishing Identically for Negative Values of the Argument

Table IIIA. Functions Not Belonging to Either of These Classes

Appendix: Distribution Functions and Their Fourier Transforms Found in the Statistical Literature

Table A. Univariate Density Functions

Table B. Univariate Discrete Distributions

Table C. Multivariate Density Functions

List of Abbreviations, Symbols, and Notations

Details

No. of pages:
180
Language:
English
Copyright:
© Academic Press 1973
Published:
Imprint:
Academic Press
eBook ISBN:
9781483219028

About the Author

Fritz Oberhettinger

About the Editor

Z. W. Birnbaum

E. Lukacs

Affiliations and Expertise

Bowling Green State University