Integral transforms and operational calculus:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Oxford [u.a.]
Pergamon Press
1965
|
| Edition: | 1. ed. |
| Series: | International series of monographs in pure and applied mathematics
78 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | 529 S. |
Staff View
MARC
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| 245 | 1 | 0 | |a Integral transforms and operational calculus |c V. A. Ditkin and A. P. Prudnikov |
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Record in the Search Index
| _version_ | 1804135986266898432 |
|---|---|
| adam_text | CONTENTS
Foreword ix
Part I
FUNDAMENTAL THEORY
Chapter 1. Fourier Transforms
§ 1 Remarks on the theory of Fourier series 3
§ 2 Fourier s integral formula 6
§ 3 Basic properties of Fourier transforms 8
§ 4 Multiple Fourier transforms 13
§ 5 Some applications of Fourier transforms 14
Chapter 8. Laplace Transforms
§ 1 The Laplace integral and its basic properties 23
§ 2 Convolution theorems 33
§ 3 Some properties of the Laplaoe transform 36
§ 4 Laplace transforms of some elementary functions 42
§ 5 Evaluation of integrals 44
§ 6 The application of Laplace transforms to the solution
of differential and integral equations 46
§ 7 Mellin transforms 69
Chapter 3. Bessel Transforms
§ 1 Hankel transforms 71
§ 2 Meijer transforms 75
§ 3 Kontorovich — Lebedev transforms 78
Chapter 4. Other Integral Transforms
§ 1 Mehler Fock transforms 82
§ 2 Hilbert transforms 85
§ 3 Laguerre transforms 86
Chapter 5. Operational Calculus
§ 1 Fundamental concepts and propositions 88
§ 2 Rational operators 94
§ 3 Laplace transformable operators 96
v
vi CONTENTS
§ 4 The realization of Laplace transformable operators 98
§ 5 Generalized Laplace transforms 101
§ 6 The field ttl 104
§ 7 Operator functions 105
§ 8 The limit of a sequence of operators. The limit
of an operator function 106
§ 9 The continuous derivative of an operator function.
The integral of an operator function 109
§ 10 Step functions 111
§ 11 Difference equations 116
§ 12 Efros transforms 120
§ 13 Operator differential equations 121
§ 14 Application of the operational calculus to the solution
of differential equations 123
§ 15 Asymptotic series 129
§ 16 The operational calculus for the operator B= 1 131
at at
Past II
TABLES OF FORMULAE
Chapter 6. Summary of Notation for Special Functions and
Certain Constants 149
Chapter 7. Fourier Cosine Transforms
§ 1 Basic formulae 164
§ 2 Rational and irrational functions 165
§ 3 Exponential functions 174
§ 4 Trigonometric functions 177
§ 5 Inverse trigonometric functions 183
§ 6 Logarithmic functions 184
§ 7 Hyperbolic functions 186
§ 8 Orthogonal polynomials 189
§ 9 The Gamma function and fuctions generated by it 192
§ 10 Integral functions 193
§11 Cylindrical functions 196
§ 12 Degenerate hypergeometric functions 239
§ 13 Spherical functions 245
§ 14 Various functions 256
Chapter 8. Fourier Sine Transforms
§ 1 Basic formulae 258
§ 2 Rational and irrational functions 259
CONTENTS Vii
§ 3 Exponential functions 268
§ 4 Trigonometric functions 272
§ 5 Inverse trigonometric functions 277
§ 6 Logarithmic functions 279
§ 7 Hyperbolic functions 281
§ 8 Orthogonal polynomials 284
§ 9 The Gamma function and functions generated by it. 290
§ 10 Integral functions 291
§ 11 Cylindrical functions 294
§ 12 Degenerate hypergeomotric functions 337
§ 13 Spherical functions 346
§ 14 Various functions 350
Chapter ». Laplace Carson Transforms
§ 1 Basic formulae 352
§ 2 Rational and irrational functions 363
§ 3 Exponential and logarithmic functions 383
§ 4 Trigonometric and hyperbolic functions. Inverse
trigonometric and inverse hyperbolic functions 389
§ 6 Cylindrical functions 400
§ 6 The Gamma function and functions generated by it.
Integral functions. Degenerate hypergeometric functions 413
§ 7 Various functions 417
Chapter 10. Mellin Transforms
§ 1 Basic formulae 422
§ 2 Various functions 423
Chapter 11. Bessel Transforms
§ 1 Hankel transforms 432
§ 1.1 Basic formulae 432
§ 1.2 Various functions 435
§ 2 Meijer transforms 461
§2.1 Basic formulae 461
§ 2.2 Various functions 463
§ 3 Bessel Y transform 478
§3.1 Basic formulae 478
§ 3.2 Various functions 479
§ 4 Bessel H transform 487
§ 4.1 Basic formulae 487
§ 4.2 Various functions 488
§ 5 Kontorovich Lebedev transforms 494
§ 6 Kon(orovich Lebedev transforms (continued) 497
Viii CONTENTS
Chapter 12. Other Integral Transforms
§ 1 Mehler Fock transforms 502
§ 2 Hilbert transforms 505
Bibliography 509
Index 623
Other Titles in the Series 527
|
| adam_txt |
CONTENTS
Foreword ix
Part I
FUNDAMENTAL THEORY
Chapter 1. Fourier Transforms
§ 1 Remarks on the theory of Fourier series 3
§ 2 Fourier's integral formula 6
§ 3 Basic properties of Fourier transforms 8
§ 4 Multiple Fourier transforms 13
§ 5 Some applications of Fourier transforms 14
Chapter 8. Laplace Transforms
§ 1 The Laplace integral and its basic properties 23
§ 2 Convolution theorems 33
§ 3 Some properties of the Laplaoe transform 36
§ 4 Laplace transforms of some elementary functions 42
§ 5 Evaluation of integrals 44
§ 6 The application of Laplace transforms to the solution
of differential and integral equations 46
§ 7 Mellin transforms 69
Chapter 3. Bessel Transforms
§ 1 Hankel transforms 71
§ 2 Meijer transforms 75
§ 3 Kontorovich — Lebedev transforms 78
Chapter 4. Other Integral Transforms
§ 1 Mehler Fock transforms 82
§ 2 Hilbert transforms 85
§ 3 Laguerre transforms 86
Chapter 5. Operational Calculus
§ 1 Fundamental concepts and propositions 88
§ 2 Rational operators 94
§ 3 Laplace transformable operators 96
v
vi CONTENTS
§ 4 The realization of Laplace transformable operators 98
§ 5 Generalized Laplace transforms 101
§ 6 The field ttl 104
§ 7 Operator functions 105
§ 8 The limit of a sequence of operators. The limit
of an operator function 106
§ 9 The continuous derivative of an operator function.
The integral of an operator function 109
§ 10 Step functions 111
§ 11 Difference equations 116
§ 12 Efros transforms 120
§ 13 Operator differential equations 121
§ 14 Application of the operational calculus to the solution
of differential equations 123
§ 15 Asymptotic series 129
§ 16 The operational calculus for the operator B= 1 131
at at
Past II
TABLES OF FORMULAE
Chapter 6. Summary of Notation for Special Functions and
Certain Constants 149
Chapter 7. Fourier Cosine Transforms
§ 1 Basic formulae 164
§ 2 Rational and irrational functions 165
§ 3 Exponential functions 174
§ 4 Trigonometric functions 177
§ 5 Inverse trigonometric functions 183
§ 6 Logarithmic functions 184
§ 7 Hyperbolic functions 186
§ 8 Orthogonal polynomials 189
§ 9 The Gamma function and fuctions generated by it 192
§ 10 Integral functions 193
§11 Cylindrical functions 196
§ 12 Degenerate hypergeometric functions 239
§ 13 Spherical functions 245
§ 14 Various functions 256
Chapter 8. Fourier Sine Transforms
§ 1 Basic formulae 258
§ 2 Rational and irrational functions 259
CONTENTS Vii
§ 3 Exponential functions 268
§ 4 Trigonometric functions 272
§ 5 Inverse trigonometric functions 277
§ 6 Logarithmic functions 279
§ 7 Hyperbolic functions 281
§ 8 Orthogonal polynomials 284
§ 9 The Gamma function and functions generated by it. 290
§ 10 Integral functions 291
§ 11 Cylindrical functions 294
§ 12 Degenerate hypergeomotric functions 337
§ 13 Spherical functions 346
§ 14 Various functions 350
Chapter ». Laplace Carson Transforms
§ 1 Basic formulae 352
§ 2 Rational and irrational functions 363
§ 3 Exponential and logarithmic functions 383
§ 4 Trigonometric and hyperbolic functions. Inverse
trigonometric and inverse hyperbolic functions 389
§ 6 Cylindrical functions 400
§ 6 The Gamma function and functions generated by it.
Integral functions. Degenerate hypergeometric functions 413
§ 7 Various functions 417
Chapter 10. Mellin Transforms
§ 1 Basic formulae 422
§ 2 Various functions 423
Chapter 11. Bessel Transforms
§ 1 Hankel transforms 432
§ 1.1 Basic formulae 432
§ 1.2 Various functions 435
§ 2 Meijer transforms 461
§2.1 Basic formulae 461
§ 2.2 Various functions 463
§ 3 Bessel Y transform 478
§3.1 Basic formulae 478
§ 3.2 Various functions 479
§ 4 Bessel H transform 487
§ 4.1 Basic formulae 487
§ 4.2 Various functions 488
§ 5 Kontorovich Lebedev transforms 494
§ 6 Kon(orovich Lebedev transforms (continued) 497
Viii CONTENTS
Chapter 12. Other Integral Transforms
§ 1 Mehler Fock transforms 502
§ 2 Hilbert transforms 505
Bibliography 509
Index 623
Other Titles in the Series 527 |
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| index_date | 2024-07-02T16:11:51Z |
| indexdate | 2024-07-09T20:49:13Z |
| institution | BVB |
| language | English Russian |
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| physical | 529 S. |
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| series | International series of monographs in pure and applied mathematics |
| series2 | International series of monographs in pure and applied mathematics |
| spelling | Ditkin, V. A. 1910-1987 Verfasser (DE-588)1045014761 aut Integral'nye preobrazovanija i operacionnoe iscislenie Integral transforms and operational calculus V. A. Ditkin and A. P. Prudnikov 1. ed. Oxford [u.a.] Pergamon Press 1965 529 S. txt rdacontent n rdamedia nc rdacarrier International series of monographs in pure and applied mathematics 78 Aus dem Russ. übers. Calculus, Operational Integral transforms Heaviside-Kalkül (DE-588)4159324-8 gnd rswk-swf Integraltransformation (DE-588)4027235-7 gnd rswk-swf Operatorenrechnung (DE-588)4389717-4 gnd rswk-swf Operatorgleichung (DE-588)4043601-9 gnd rswk-swf Operatorgleichung (DE-588)4043601-9 s DE-604 Heaviside-Kalkül (DE-588)4159324-8 s Integraltransformation (DE-588)4027235-7 s 1\p DE-604 Operatorenrechnung (DE-588)4389717-4 s 2\p DE-604 Prudnikov, A. P. 1927-1999 Verfasser (DE-588)123364825 aut International series of monographs in pure and applied mathematics 78 (DE-604)BV001888024 78 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015226381&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ditkin, V. A. 1910-1987 Prudnikov, A. P. 1927-1999 Integral transforms and operational calculus International series of monographs in pure and applied mathematics Calculus, Operational Integral transforms Heaviside-Kalkül (DE-588)4159324-8 gnd Integraltransformation (DE-588)4027235-7 gnd Operatorenrechnung (DE-588)4389717-4 gnd Operatorgleichung (DE-588)4043601-9 gnd |
| subject_GND | (DE-588)4159324-8 (DE-588)4027235-7 (DE-588)4389717-4 (DE-588)4043601-9 |
| title | Integral transforms and operational calculus |
| title_alt | Integral'nye preobrazovanija i operacionnoe iscislenie |
| title_auth | Integral transforms and operational calculus |
| title_exact_search | Integral transforms and operational calculus |
| title_exact_search_txtP | Integral transforms and operational calculus |
| title_full | Integral transforms and operational calculus V. A. Ditkin and A. P. Prudnikov |
| title_fullStr | Integral transforms and operational calculus V. A. Ditkin and A. P. Prudnikov |
| title_full_unstemmed | Integral transforms and operational calculus V. A. Ditkin and A. P. Prudnikov |
| title_short | Integral transforms and operational calculus |
| title_sort | integral transforms and operational calculus |
| topic | Calculus, Operational Integral transforms Heaviside-Kalkül (DE-588)4159324-8 gnd Integraltransformation (DE-588)4027235-7 gnd Operatorenrechnung (DE-588)4389717-4 gnd Operatorgleichung (DE-588)4043601-9 gnd |
| topic_facet | Calculus, Operational Integral transforms Heaviside-Kalkül Integraltransformation Operatorenrechnung Operatorgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015226381&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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