Integrals of Bessel Functions

Name: Integrals of Bessel Functions
Brand: Dover Publications
Price: 36.99 EUR
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Yudell L. Luke(Autor*in)

Dover Publications (Verlag)

Erschienen am 20. Oktober 2014

442 Seiten

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Inhalt

Cover
Title Page
Copyright Page
Dedication
Preface
Contents
Chapter I: BASIC FORMULAS
1.1. Introduction
1.2. The Gamma Function and Related Functions
1.3. Generalized Hypergeometric Series
1.3.1 Definition and Basic Properties
1.3.2 Integral Representations
1.3.3 Asymptotic Expansions
1.3.4 The Form of for Special Values of the Parameters
1.3.5 Special Values of Hypergeometric Functions
1.3.6 Expansion of Hypergeometric Functions in Series of Hypergeometric Functions
1.4. Bessel Functions
1.4.1. Power Series Expansions and Connecting Formulae
1.4.2. Expansions in Series of Bessel Functions
1.4.3. Difference-Differential Properties
1.4.4. Wronskians
1.4.5. Integral Representations
1.4.6. Asymptotic Expansions for Large z
1.4.7. Polynomial Approximations
1.4.8. Description of Mathematical Tables
Chapter II: INTEGRALS OF THE TYPE
2.1. Definitions and Connecting Formulae
2.2. Differential-Difference Properties
2.3. Power Series Expansions
2.4. Expansions in Series of Bessel Functions
2.5. Asymptotic Expansions for Large z
2.6. Infinite Integrals
2.7. Circular Representations of Jn(z) and
2.8. Polynomial Approximations
2.9. Description of Mathematical Tables
Chapter III: REPRESENTATIONS OF IN TERMS OF LOMMEL FUNCTIONS
3.1. A Theorem on Indefinite Integrals Involving a Bessel Function
3.2. Lommel Functions
3.3. Recurrence Relations
3.4. Formulae for When Is Not Defined
3.5. Integral Representatlons
3.6. Expansions in Series of Bessel Functions
3.7. Lommel Functions and Struve Functions
3.8. Anger-Weber Functions
3.9. and Formulae for Tabulated Functions
3.10. Fourier-Bessel Coefficients
3.11. Polynomial Approximations
3.12. Description of Mathematical Tables
Chapter IV: AND AN ASSOCIATED BESSEL FUNCTION
4.1. Introduction
4.2. Power Series Expansions and Connecting Formulae
4.3. Expansions in Series of Bessel Functions
4.4. Asymptotic Expansions for Large z
4.5. Infinite Integrals
4.6. An Associated Bessel Function
4.7. Recurrence Relations
4.8. Integral Representations
4.9. Formulae for When Is Not Defined
4.10. Expansions of and in Series of Bessel Functions
4.11. Associated Bessel Function Representations for and Related Integrals
4.12. Description of Mathematical Tables
Chapter V: REDUCTION FORMULAS FOR
5.1. General Development
5.2. Evaluation of for the Special Values of the Parameters
Chapter VI: AIRY FUNCTIIONS
6.1. Introduction
6.2. Airy Integrals
6.2.1. Definitions
6.2.2. Derivatives
6.2.3. Interrelations
6.2.4. Differential Equation and Wronskian
6.2.5. Power Series
6.2.6. Asymptotic Expansions
6.2.7. Integral Representations
6.3. Integrals of Airy Integrals
6.3.1. Relations to Other Functions and Interrelations
6.3.2. Power Series Expansions
6.3.3. Convergent Expansions in Terms of Lommel Functions
6.3.4. Expansions in Series of Bessel Functions
6.3.5. Asymptotic Expansions
6.4. The Integrals of Gi (z) and Hi(-z)
6.5. Description of Mathematical Tables
Chapter VII: INCOMPLETE GAMMA FUNCTION AND RELATED FUNCTIONS
7.1. Introduction
7.2. Elementary Properties
7.3. Integral Representations
7.4. Asymptotic Expansions for Large z
7.5. Infinite Integrals
7.6. Expansions in Series of Bessel Functions
7.7. Rational Approximations, Continued Fractions, Inequalities
7.8. The Exponential Integral
7.9. Sine and Cosine Integrals
7.10. Error Functions.
7.11. Fresnel Integrals
7.12. Indefinite and Definite Integrals Associated with the Incomplete Gamma Function and Related Functions
7.13. Description of Mathematical Tables
Chapter VIII: REPEATED INTEGRALS OF BESSEL FUNCTIONS
8.1. Introduction
8.2. Power Series Expansions and Differential Equations
8.3. Recurrence Equations
8.4. Asymptotic Expansions for Large z
8.5. Infinite Integrals
8.6. Further Representations
8.7. Asymptotic Expansions f or Large Parameters
8.8. Exponential Series Representations for
Chapter IX: INTEGRALS INVOLVING STRUVE FUNCTIONS
9.1. Introduction
9.2. Power Series Expansions
9.3. Asymptotic Expansions for Large z
9.4. Infinite Integrals
9.5. Reduction Formulas
9.6. The Complete Cicala Function
9.7. Description of Mathematical Tables
Chapter X: SCHWARZ FUNCTIONS AND GENERALIZATIONS
10.1. Introduction
10.2. Power Series Expansions
10.3. Expansions in Series of Bessel Functions
10.4. Representation in Series of Circular Functions
10.5. Asymptotic Expansions for Large z
10.6. Infinite Integrals
10.7. Description of Mathematical Tables
Chapter XI: INTEGRALS INVOLVING PRODUCTS OF BESSEL FUNCTIONS AND STRUVE FUNCTIONS
11.1. A General Theorem for the Evaluation of Indefinite Integrals
11.2. Integrals Involving the Product of Two Bessel Functions
11.3. Integrals Involving the Product of a Bessel Function and a Struve Function
11.4. Integrals Involving the Product of Two Struve Functions
11.5. Integrals Deduced from Wronskians
11.6. An Integral Involving the Product of Three Bessel Functions
Chapter XII: MISCELLANEOUS INDEFINITE INTEGRALS INVOLVING BESSEL FUNCTIONS
12.1. The Integral J(x,y)
12.1.1. Introduction
12.1.2. Partial Differential Equations
12.1.3. Power Series Expansions and Expansions in Series of Bessel Functions
12.1.4. Laplace Transform and Integral Representations
12.1.5. Asymptotic Expansions
12.1.6. Integrals Related to J(x,y)
12.1.7. Description of Mathematical Tables and Approximations
12.2. A General Theorem for Representing an Indefinite Integral Involving Bessel Functions in Series of Bessel Functions
12.3. Other Indefinite Integrals
Chapter XIII: DEFINITE INTEGRALS
13.1. Introduction
13.2. Orthogonality Properties of Bessel Functions
13.3. Finite Integrals
13.3.1. Convolution Integrals
13.3.2. Integrals Involving Bessel Functions with Trigonometric Argument
13.3.3. Lommel's Functions of Two Variables
13.4. Infinite Integrals
13.4.1. Integrals with Exponential Functions
13.4.2. Weber-Schafheitlin Type Integrals
13.4.3. Sonine-Gegenbauer Type Integrals
13.4.4. Hankel-Nicholson Type Integrals
13.4.5. Integrals Involving the Products of Three or More Bessel Functions
13.4.6. Miscellaneous Integrals
13.4.7. Integrals with Respect to the Order
13.4.8. Dual and Triple Integral Equations
Chapter XIV: TABLES OF BESSEL FUNCTIONS AND INTEGRALS OF BESSEL FUNCTIONS
Introduction
Table I.
Table II.
Table III.
Table IV.
Table V.
Table VI.
Table VII.
Table VIII.
Table IX.
Table X.
Table XI. Integrals of Jo(x) and Yo(x)
Table XII. Integrals of Io(x) and Ko(x)
Bibliography
Index of Notations
Author Index
Subject Index

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