Tables of Fourier Transforms and Fourier Transforms of Distributions

by Fritz Oberhettinger

Overview

This book presents a collection of integrals of the sine-, cosine- and exponential Fourier transforms of functions f(x). It is the second, considerably enlarged version of the author's previous publication "Tabellen zur Fourier Transformation" (Springer-Verlag 1957). In addition to numerous new results in Parts I-III, a new Part IV has been introduced dealing with problems in mathematical statistics. The aim of the book is to serve as a reference work for all those whose main interest is in the application of Fourier transform methods. These methods have found a wide variety of applications in the natural and technical sciences.

Product Details

ISBN-13:	9783540506300
Publisher:	Springer Berlin Heidelberg
Publication date:	05/18/1990
Edition description:	Softcover reprint of the original 1st ed. 1990
Pages:	259
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

I. Fourier Cosine Transforms (Tables I).- 1.1 Algebraic Functions.- 1.2 Arbitrary Powers.- 1.3 Exponential Functions.- 1.4 Logarithmic Functions.- 1.5 Trigonometric Functions.- 1.6 Inverse Trigonometric Functions.- 1.7 Hyperbolic Functions.- 1.8 Orthogonal Polynomials.- 1.9 Gamma- and Related Functions.- 1.10 The Error- and the Fresnel Integrals.- 1.11 The Exponential- and Related Integrals.- 1.12 Legendre Functions.- 1.13 Bessel Functions of Arguments x, x2 and 1/x.- 1.14 Bessel Functions of Argument (ax2 + bx + c)1/2.- 1.15 Bessel Functions of Trigonometric and Hyperbolic Arguments.- 1.16 Bessel Functions of Variable Order.- 1.17 Modified Bessel Functions of Arguments x, x2 and 1/x.- 1.18 Modified Bessel Functions of Argument (ax2 + bx + c)1/2.- 1.19 Modified Bessel Functions of Trigonometric and Hyperbolic Arguments.- 1.20 Modified Bessel Functions of Variable Order.- 1.21 Functions Related to Bessel Functions.- 1.22 Parabolic Cylinder- and Whittaker Functions.- 1.23 Elliptic Integrals.- II. Fourier Sine Transforms (Tables II).- 2.1 Algebraic Functions.- 2.2 Arbitrary Powers.- 2.3 Exponential Functions.- 2.4 Logarithmic Functions.- 2.5 Trigonometric Functions.- 2.6 Inverse Trigonometric Functions.- 2.7 Hyperbolic Functions.- 2.8 Orthogonal Polynomials.- 2.9 Gamma- and Related Functions.- 2.10 The Error- and the Fresnel Integrals.- 2.11 The Exponential- and Related Integrals.- 2.12 Legendre Functions.- 2.13 Bessel Functions of Arguments x, x2 and 1/x.- 2.14 Bessel Functions of Argument (ax2 + bx + c)1/2.- 2.15 Bessel Functions of Trigonometric and Hyperbolic Arguments.- 2.16 Bessel Functions of Variable Order.- 2.17 Modified Bessel Functions of Arguments x, x2 and 1/x.- 2.18 Modified Bessel Functions of Argument (ax2 + bx + c)1/2.- 2.19 Modified Bessel Functions of Trigonometric and Hyperbolic Arguments.- 2.20 Modified Bessel Functions of Variable Order.- 2.21 Functions Related to Bessel Functions.- 2.22 Parabolic Cylinder- and Whittaker Functions.- 2.23 Elliptic Integrals.- III. Exponential Fourier Transforms (Tables III).- IV. Fourier Transforms of Distributions (Tables IV and V).- List of Functions.

Editorial Reviews

Corrected and expanded revision of a handbook first published (in German) in 1957, to which the author has added (as Part IV) thirty- seven pages of material specific to the Fourier transform properties of statistical distribution functions. Reasonably priced and useful. (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)

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