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Integrals of Bessel Functions [Pehme köide]

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  • Formaat: Paperback / softback, 432 pages, kõrgus x laius x paksus: 234x157x22 mm, kaal: 594 g
  • Ilmumisaeg: 30-Jan-2015
  • Kirjastus: Dover Publications Inc.
  • ISBN-10: 0486789691
  • ISBN-13: 9780486789699
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Integrals of Bessel FunctionsSuurem pilt
  • Formaat: Paperback / softback, 432 pages, kõrgus x laius x paksus: 234x157x22 mm, kaal: 594 g
  • Ilmumisaeg: 30-Jan-2015
  • Kirjastus: Dover Publications Inc.
  • ISBN-10: 0486789691
  • ISBN-13: 9780486789699
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780486789699.html
Märksõnad:
Luke explains how researchers can evaluate definite and indefinite integrals involving Bessel functions, which is required in many applied problems. Other books on integrals involving Bessel functions mostly discuss definite integrals, and though he also treats definite integrals, he emphasizes indefinite ones. He begins by discussing generalized hypergeometric functions, of which Bessel functions are a special case, then applies the results to many useful representation of Bessel functions and their integrals by specializing the parameters. Some of the results could also be applied to other hypergeometric functions, he says. Annotation ©2015 Ringgold, Inc., Portland, OR (protoview.com)

A massive compendium of useful information, this volume represents a valuable tool for applied mathematicians in many areas of academia and industry. A dozen useful tables supplement the text. 1962 edition.


Integrals of Bessel Functions concerns definite and indefinite integrals, the evaluation of which is necessary to numerous applied problems. A massive compendium of useful information, this volume represents a resource for applied mathematicians in many areas of academia and industry as well as an excellent text for advanced undergraduates and graduate students of mathematics.
Starting with an extensive introductory chapter on basic formulas, the treatment advances to indefinite integrals, examining them in terms of Lommel and Bessel functions. Subsequent chapters explore airy functions, incomplete gamma function and related functions, repeated integrals of Bessel functions, and integrals involving Struve functions. Additional topics include Schwarz functions and generalizations, miscellaneous indefinite integrals involving Bessel functions, and definite integrals. A dozen useful tables supplement the text.
Preface iii
Chapter I Basic Formulas
1.1 Introduction
1(1)
1.2 The Gamma Function and Related Functions
2(2)
1.3 Generalized Hypergeometric Series
4(18)
1.3.1 Definition and Basic Properties
4(1)
1.3.2 Integral Representations
5(2)
1.3.3 Asymptotic Expansions
7(7)
1.3.4 The Form of Lp,q(z) for Special Values of the Parameters
14(4)
1.3.5 Special Values of Hypergeometric Functions
18(1)
1.3.6 Expansion of Hypergeometric Functions in Series of Hypergeometric Functions
19(3)
1.4 Bessel Functions
22(20)
1.4.1 Power Series Expansions and Connecting Formulae
22(3)
1.4.2 Expansions in Series of Bessel Functions
25(2)
1.4.3 Difference-Differential Properties
27(2)
1.4.4 Wronskians
29(1)
1.4.5 Integral Representations
30(1)
1.4.6 Asymptotic Expansions for Large z
31(2)
1.4.7 Polynomial Approximations
33(7)
1.4.8 Description of Mathematical Tables
40(2)
Chapter II Integrals Of The Type
2.1 Definitions and Connecting Formulae
42(2)
2.2 Differential-Difference Properties
44(1)
2.3 Power Series Expansions
44(7)
2.4 Expansions in Series of Bessel Functions
51(2)
2.5 Asymptotic Expansions for Large z
53(3)
2.6 Infinite Integrals
56(1)
2.7 Circular Representations of Jn(z) and Jn(t)dt
57(3)
2.8 Polynomial Approximations
60(9)
2.9 Description of Mathematical Tables
69(4)
Chapter III Representations Of In Terms Of Lommel Functions
3.1 A Theorem on Indefinite Integrals Involving a Bessel Function
73(1)
3.2 Lommel Functions
74(1)
3.3 Recurrence Relations
75(1)
3.4 Formulae for Sμ,v(z) When sμ,v(z) Is Not Defined
76(1)
3.5 Integral Representations
77(2)
3.6 Expansions in Series of Bessel Functions
79(1)
3.7 Lommel Functions and Struve Functions
80(3)
3.8 Anger-Weber Functions
83(2)
3.9 tμwv(t)dt and Formulae for Tabulated Functions
85(4)
3.10 Fourier-Bessel Coefficients
89(3)
3.11 Polynomial Approximations
92(2)
3.12 Description of Mathematical Tables
94(1)
Chapter IV An Associated Bessel Function
4.1 Introduction
95(1)
4.2 Power Series Expansions and Connecting Formulae
95(5)
4.3 Expansions in Series of Bessel Functions
100(1)
4.4 Asymptotic Expansions for Large z
101(5)
4.5 Infinite Integrals
106(1)
4.6 An Associated Bessel Function
107(3)
4.7 Recurrence Relations
110(1)
4.8 Integral Representations
110(2)
4.9 Formulae for Hμ,v(z) When hμ,v(z) Is Not Defined
112(3)
4.10 Expansions of hμv(z) and Hμ,v(z) in Series of Bessel Functions
115(2)
4.11 Associated Bessel Function Representations for e-'ttμkv(t)dt and,-Related Integrals
117(2)
4.12 Description of Mathematical Tables
119(1)
Chapter V Reduction Formulas
5.1 General Development
120(1)
5.2 Evaluation of e-pttμWv(λt)dt for Special Values of the Parameters
121(6)
Chapter VI Airy Functions
6.1 Introduction
127(1)
6.2 Airy Integrals
127(5)
6.2.1 Definitions
127(1)
6.2.2 Derivatives
127(1)
6.2.3 Interrelations
128(1)
6.2.4 Differential Equation and Wronskian
128(1)
6.2.5 Power Series
129(1)
6.2.6 Asymptotic Expansions
129(2)
6.2.7 Integral Representations
131(1)
6.3 Integrals of Airy Integrals
132(8)
6.3.1 Relations to Other Functions and Interrelations
132(1)
6.3.2 Power Series Expansions
133(1)
6.3.3 Convergent Expansions in Terms of Lommel Functions
133(2)
6.3.4 Expansions in Series of Bessel Functions
135(1)
6.3.5 Asymptotic Expansions
136(4)
6.4 The Integrals of Gi(z) and Hi(-z)
140(1)
6.5 Description of Mathematical Tables
141(3)
Chapter VII Incomplete Gamma Function And Related Functions
7.1 Introduction
144(1)
7.2 Elementary Properties
145(1)
7.3 Integral Representations
146(1)
7.4 Asymptotic Expansions for Large z
146(1)
7.5 Infinite Integrals
147(1)
7.6 Expansions in Series of Bessel Functions
148(4)
7.7 Rational Approximations, Continued Fractions, Inequalities
152(11)
7.8 The Exponential Integral
163(5)
7.9 Sine and Cosine Integrals
168(4)
7.10 Error Functions
172(7)
7.11 Fresnel Integrals
179(3)
7.12 Indefinite and Definite Integrals Associated with the Incomplete Gamma Function and Related Functions
182(5)
7.13 Description of Mathematical Tables
187(8)
Chapter VIII Repeated Integrals Of Bessel Functions
8.1 Introduction
195(4)
8.2 Power Series Expansions and Differential Equations
199(12)
8.3 Recurrence Equations
211(1)
8.4 Asymptotic Expansions for Large z
212(4)
8.5 Infinite Integrals
216(1)
8.6 Further Representations
217(2)
8.7 Asymptotic Expansions for Large Parameters
219(2)
8.8 Exponential Series Representations for Kα,v(z)
221(2)
Chapter IX Integrals Involving Struve Functions
9.1 Introduction
223(1)
9.2 Power Series Expansions
223(1)
9.3 Asymptotic Expansions for Large z
224(2)
9.4 Infinite Integrals
226(1)
9.5 Reduction Formulas
227(4)
9.6 The Complete Cicala Function
231(1)
9.7 Description of Mathematical Tables
232(2)
Chapter X Schwarz Functions And Generalizations
10.1 Introduction
234(1)
10.2 Power Series Expansions
234(4)
10.3 Expansions in Series of Bessel Functions
238(3)
10.4 Representation in Series of Circular Functions
241(2)
10.5 Asymptotic Expansions for Large z
243(3)
10.6 Infinite Integrals
246(5)
10.7 Description of Mathematical Tables
251(2)
Chapter XI Integrals Involving Products Of Bessel Functions And Struve Functions
11.1 A General Theorem for the Evaluation of Indefinite Integrals
253(1)
11.2 Integrals Involving the Product of Two Bessel Functions
254(10)
11.3 Integrals Involving the Product of a Bessel Function and a Struve Function
264(2)
11.4 Integrals Involving the Product of Two Struve Functions
266(2)
11.5 Integrals Deduced from Wronskians
268(1)
11.6 An Integral Involving the Product of Three Bessel Functions
269(2)
Chapter XII Miscellaneous Indefinite Integrals Involving Bessel Functions
12.1 The Integral J(x,y)
271(12)
12.1.1 Introduction
271(1)
12.1.2 Partial Differential Equations
272(3)
12.1.3 Power Series Expansions and Expansions in Series of Bessel Functions
275(1)
12.1.4 Laplace Transform and Integral Representations
276(2)
12.1.5 Asymptotic Expansions
278(2)
12.1.6 Integrals Related to J(x,y)
280(2)
12.1.7 Description of Mathematical Tables and Approximations
282(1)
12.2 A General Theorem for Representing an Indefinite Integral Involving Bessel Functions in Series of Bessel Functions
283(6)
12.3 Other Indefinite Integrals
289(1)
Chapter XIII Definite Integrals
13.1 Introduction
290(1)
13.2 Orthogonality Properties of Bessel Functions
290(2)
13.3 Finite Integrals
292(20)
13.3.1 Convolution Integrals
292(1)
13.3.2 Integrals Involving Bessel Functions with Trigonometric Argument
293(15)
13.3.3 Lommel's Functions of Two Variables
308(4)
13.4 Infinite Integrals
312(37)
13.4.1 Integrals with Exponential Functions
312(12)
13.4.2 Weber-Schafheitlin Type Integrals
324(3)
13.4.3 Sonine-Gegenbauer Type Integrals
327(3)
13.4.4 Hankel-Nicholson Type Integrals
330(1)
13.4.5 Integrals Involving the Products of Three or More Bessel Functions
331(4)
13.4.6 Miscellaneous Integrals
335(5)
13.4.7 Integrals with Respect to the Order
340(2)
13.4.8 Dual and Triple Integral Equations
342
Chapter XIV Tables Of Bessel Functions And Integrals Of Bessel Functions
Introduction
349(1)
Table I. Jn(x) , Yn(x) , n = 0,1
350(3)
Table II. e-xIn(x) , exKn(x) , n = 0,1 , ex
353(3)
Table III. Jn(x) , n = 2(1)6
356(3)
Table IV. e-xIn(x) , n = 2(1)6
359(3)
Table V. (π/2x)jn_i(x) , n = 0(1)4
362(3)
Table VI. Tv(x) , v = ±1/4 ±3/4
365(3)
Table VII. Jp(x) , v = ±1/3 , ±2/3
368(3)
Table VIII. x-(n+1)In+1/2(x) , e-xIn+1/2(x) , n = 0(1)4
371(3)
Table IX. Iv(x) , v = ±1/4 , ±3/4
374(3)
Table X. Iv(x) , v = ±1/3 , ±2/3
377(3)
Table XI. Integrals of Jo(x) and Yo(x)
380(3)
Table XII. Integrals of Io(x) and Ko(x)
383(3)
Bibliography 386(18)
Index of Notations 404(6)
Author Index 410(4)
Subject Index 414