Integral transforms and their applications:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2007
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Publisher description Inhaltsverzeichnis |
| Beschreibung: | 700 S. graph. Darst. |
| ISBN: | 9781584885757 1584885750 |
Internformat
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| 245 | 1 | 0 | |a Integral transforms and their applications |c Lokenath Debnath ; Dambaru Bhatta |
| 250 | |a 2. ed. | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | INTEGRAL TRANSFORMS AND THEIR APPLICATIONS SECOND EDITION LOKENATH
DEBNATH DAMBARU BHATTA ^IJCHAPMAN & HALL/CRC M M TAYLOR & FRANCIS GROUP
BOCA RATON LONDON NEW YORK CHAPMAN & HALL/CRC IS AN IMPRINT OF THE
TAYLOR & FRANCIS GROUP, AN INFORMA BUSINESS CONTENTS 1 INTEGRAL
TRANSFORMS 1 1.1 BRIEF HISTORICAL INTRODUCTION 1 1.2 BASIC CONCEPTS AND
DEFINITIONS 6 2 FOURIER TRANSFORMS AND THEIR APPLICATIONS 9 2.1
INTRODUCTION 9 2.2 THE FOURIER INTEGRAL FORMULAS 10 2.3 DEFINITION OF
THE FOURIER TRANSFORM AND EXAMPLES 12 2.4 FOURIER TRANSFORMS OF
GENERALIZED FUNCTIONS 17 2.5 BASIC PROPERTIES OF FOURIER TRANSFORMS 28
2.6 POISSON S SUMMATION FORMULA 37 2.7 THE SHANNON SAMPLING THEOREM 44
2.8 GIBBS PHENOMENON 54 2.9 HEISENBERG S UNCERTAINTY PRINCIPLE 57 2.10
APPLICATIONS OF FOURIER TRANSFORMS TO ORDINARY DIFFERENTIAL EQUATIONS 60
2.11 SOLUTIONS OF INTEGRAL EQUATIONS 65 2.12 SOLUTIONS OF PARTIAL
DIFFERENTIAL EQUATIONS 68 2.13 FOURIER COSINE AND SINE TRANSFORMS WITH
EXAMPLES 91 2.14 PROPERTIES OF FOURIER COSINE AND SINE TRANSFORMS 93
2.15 APPLICATIONS OF FOURIER COSINE AND SINE TRANSFORMS TO PARTIAL
DIFFERENTIAL EQUATIONS 96 2.16 EVALUATION OF DEFINITE INTEGRALS 100 2.17
APPLICATIONS OF FOURIER TRANSFORMS IN MATHEMATICAL STATISTICS 103 2.18
MULTIPLE FOURIER TRANSFORMS AND THEIR APPLICATIONS 109 2.19 EXERCISES
119 3 LAPLACE TRANSFORMS AND THEIR BASIC PROPERTIES 133 3.1 INTRODUCTION
133 3.2 DEFINITION OF THE LAPLACE TRANSFORM AND EXAMPLES 134 3.3
EXISTENCE CONDITIONS FOR THE LAPLACE TRANSFORM 139 3.4 BASIC PROPERTIES
OF LAPLACE TRANSFORMS 140 3.5 THE CONVOLUTION THEOREM AND PROPERTIES OF
CONVOLUTION . . 145 3.6 DIFFERENTIATION AND INTEGRATION OF LAPLACE
TRANSFORMS .... 151 3.7 THE INVERSE LAPLACE TRANSFORM AND EXAMPLES 154
3.8 TAUBERIAN THEOREMS AND WATSON S LEMMA 168 3.9 EXERCISES 173 4
APPLICATIONS OF LAPLACE TRANSFORMS 181 4.1 INTRODUCTION 181 4.2
SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS 182 4.3 PARTIAL
DIFFERENTIAL EQUATIONS, INITIAL AND BOUNDARY VALUE PROBLEMS 207 4.4
SOLUTIONS OF INTEGRAL EQUATIONS 222 4.5 SOLUTIONS OF BOUNDARY VALUE
PROBLEMS 225 4.6 EVALUATION OF DEFMITE INTEGRALS 228 4.7 SOLUTIONS OF
DIFFERENCE AND DIFFERENTIAL-DIFFERENCE EQUATIONS . 230 4.8 APPLICATIONS
OF THE JOINT LAPLACE AND FOURIER TRANSFORM . . . 237 4.9 SUMMATION OF
INFINITE SERIES 248 4.10 TRANSFER FUNCTION AND IMPULSE RESPONSE FUNCTION
OF A LINEAR SYSTEM 251 4.11 EXERCISES 256 5 FRACTIONAL CALCULUS AND ITS
APPLICATIONS 269 5.1 INTRODUCTION 269 5.2 HISTORICAL COMMENTS 270 5.3
FRACTIONAL DERIVATIVES AND INTEGRALS 272 5.4 APPLICATIONS OF FRACTIONAL
CALCULUS 279 5.5 EXERCISES 282 6 APPLICATIONS OF INTEGRAL TRANSFORMS TO
FRACTIONAL DIFFERENTIAL AND INTEGRAL EQUATIONS 283 6.1 INTRODUCTION 283
6.2 LAPLACE TRANSFORMS OF FRACTIONAL INTEGRALS AND FRACTIONAL
DERIVATIVES 284 6.3 FRACTIONAL ORDINARY DIFFERENTIAL EQUATIONS 287 6.4
FRACTIONAL INTEGRAL EQUATIONS 290 6.5 INITIAL VALUE PROBLEMS FOR
FRACTIONAL DIFFERENTIAL EQUATIONS . 295 6.6 GREEN S FUNCTIONS OF
FRACTIONAL DIFFERENTIAL EQUATIONS . . . . 298 6.7 FRACTIONAL PARTIAL
DIFFERENTIAL EQUATIONS 299 6.8 EXERCISES 312 7 HANKEL TRANSFORMS AND
THEIR APPLICATIONS 315 7.1 INTRODUCTION 315 7.2 THE HANKEL TRANSFORM AND
EXAMPLES 316 7.3 OPERATIONAL PROPERTIES OF THE HANKEL TRANSFORM 319 7.4
APPLICATIONS OF HANKEL TRANSFORMS TO PARTIAL DIFFERENTIAL EQUATIONS 322
7.5 EXERCISES 331 8 MELLIN TRANSFORMS AND THEIR APPLICATIONS 339 8.1
INTRODUCTION 339 8.2 DEFINITION OF THE MELLIN TRANSFORM AND EXAMPLES 340
8.3 BASIC OPERATIONAL PROPERTIES OF MELLIN TRANSFORMS 343 8.4
APPLICATIONS OF MELLIN TRANSFORMS 349 8.5 MELLIN TRANSFORMS OF THE WEYL
FRACTIONAL INTEGRAL AND THE WEYL FRACTIONAL DERIVATIVE 353 8.6
APPLICATION OF MELLIN TRANSFORMS TO SUMMATION OF SERIES . . 358 8.7
GENERALIZED MELLIN TRANSFORMS 361 8.8 EXERCISES 365 9 HUBERT AND
STIELTJES TRANSFORMS 371 9.1 INTRODUCTION 371 9.2 DEFINITION OF THE
HUBERT TRANSFORM AND EXAMPLES 372 9.3 BASIC PROPERTIES OF HUBERT
TRANSFORMS 375 9.4 HUBERT TRANSFORMS IN THE COMPLEX PLANE 378 9.5
APPLICATIONS OF HUBERT TRANSFORMS 380 9.6 ASYMPTOTIC EXPANSIONS OF
ONE-SIDED HUBERT TRANSFORMS . . . 388 9.7 DEFINITION OF THE STIELTJES
TRANSFORM AND EXAMPLES 391 9.8 BASIC OPERATIONAL PROPERTIES OF STIELTJES
TRANSFORMS 394 9.9 INVERSION THEOREMS FOR STIELTJES TRANSFORMS 396 9.10
APPLICATIONS OF STIELTJES TRANSFORMS 399 9.11 THE GENERALIZED STIELTJES
TRANSFORM 401 9.12 BASIC PROPERTIES OF THE GENERALIZED STIELTJES
TRANSFORM .... 403 9.13 EXERCISES 404 10 FINITE FOURIER SINE AND COSINE
TRANSFORMS 407 10.1 INTRODUCTION 407 10.2 DEFINITIONS OF THE FINITE
FOURIER SINE AND COSINE TRANSFORMS AND EXAMPLES 408 10.3 BASIC
PROPERTIES OF FINITE FOURIER SINE AND COSINE TRANSFORMS 410 10.4
APPLICATIONS OF FINITE FOURIER SINE AND COSINE TRANSFORMS . . 416 10.5
MULTIPLE FINITE FOURIER TRANSFORMS AND THEIR APPLICATIONS . 422 10.6
EXERCISES 425 11 FINITE LAPLACE TRANSFORMS 429 11.1 INTRODUCTION 429
11.2 DEFINITION OF THE FINITE LAPLACE TRANSFORM AND EXAMPLES . . 430
11.3 BASIC OPERATIONAL PROPERTIES OF THE FINITE LAPLACE TRANSFORM 436
11.4 APPLICATIONS OF FINITE LAPLACE TRANSFORMS 439 11.5 TAUBERIAN
THEOREMS 443 11.6 EXERCISES 443 12 Z TRANSFORMS 445 12.1 INTRODUCTION
445 12.2 DYNAMIC LINEAR SYSTEMS AND IMPULSE RESPONSE 445 12.3 DEFINITION
OF THE Z TRANSFORM AND EXAMPLES 449 12.4 BASIC OPERATIONAL PROPERTIES OF
Z TRANSFORMS 453 12.5 THE INVERSE Z TRANSFORM AND EXAMPLES 459 12.6
APPLICATIONS OF Z TRANSFORMS TO FINITE DIFFERENCE EQUATIONS . 463 12.7
SUMMATION OF INFINITE SERIES 466 12.8 EXERCISES 469 13 FINITE HANKEL
TRANSFORMS 473 13.1 INTRODUCTION 473 13.2 DEFINITION OF THE FINITE
HANKEL TRANSFORM AND EXAMPLES . . . 473 13.3 BASIC OPERATIONAL
PROPERTIES 476 13.4 APPLICATIONS OF FINITE HANKEL TRANSFORMS 476 13.5
EXERCISES 481 14 LEGENDRE TRANSFORMS 485 14.1 INTRODUCTION 485 14.2
DEFINITION OF THE LEGENDRE TRANSFORM AND EXAMPLES 486 14.3 BASIC
OPERATIONAL PROPERTIES OF LEGENDRE TRANSFORMS 489 14.4 APPLICATIONS OF
LEGENDRE TRANSFORMS TO BOUNDARY VALUE PROBLEMS 497 14.5 EXERCISES 498 15
JACOBI AND GEGENBAUER TRANSFORMS 501 15.1 INTRODUCTION 501 15.2
DEFINITION OF THE JACOBI TRANSFORM AND EXAMPLES 501 15.3 BASIC
OPERATIONAL PROPERTIES 504 15.4 APPLICATIONS OF JACOBI TRANSFORMS TO THE
GENERALIZED HEAT CONDUCTION PROBLEM 505 15.5 THE GEGENBAUER TRANSFORM
AND ITS BASIC OPERATIONAL PROPERTIES 507 15.6 APPLICATION OF THE
GEGENBAUER TRANSFORM 510 16 LAGUERRE TRANSFORMS 511 16.1 INTRODUCTION
511 16.2 DEFINITION OF THE LAGUERRE TRANSFORM AND EXAMPLES 511 16.3
BASIC OPERATIONAL PROPERTIES 516 16.4 APPLICATIONS OF LAGUERRE
TRANSFORMS 520 16.5 EXERCISES 523 17 HERMITE TRANSFER MS 525 17.1
INTRODUCTION 525 17.2 DEFINITION OF THE HERMITE TRANSFORM AND EXAMPLES
526 17.3 BASIC OPERATIONAL PROPERTIES 529 17.4 EXERCISES 538 18 THE
RADON TRANSFORM AND ITS APPLICATIONS 539 18.1 INTRODUCTION 539 18.2 THE
RADON TRANSFORM 541 18.3 PROPERTIES OF THE RADON TRANSFORM 545 18.4 THE
RADON TRANSFORM OF DERIVATIVES 550 18.5 DERIVATIVES OF THE RADON
TRANSFORM 551 18.6 CONVOLUTION THEOREM FOR THE RADON TRANSFORM 553 18.7
INVERSE OF THE RADON TRANSFORM AND THE PARSEVAL RELATION . . 554 18.8
APPLICATIONS OF THE RADON TRANSFORM 560 18.9 EXERCISES 561 19 WAVELETS
AND WAVELET TRANSFORMS 563 19.1 BRIEF HISTORICAL REMARKS 563 19.2
CONTINUOUS WAVELET TRANSFORMS 565 19.3 THE DISCRETE WAVELET TRANSFORM
573 19.4 EXAMPLES OF ORTHONORMAL WAVELETS 575 19.5 EXERCISES 584
APPENDIX A SOME SPECIAL FUNCTIONS AND THEIR PROPERTIES 587 A-L GAMMA,
BETA, AND ERROR FUNCTIONS 587 A-2 BESSEL AND AIRY FUNCTIONS 592 A-3
LEGENDRE AND ASSOCIATED LEGENDRE FUNCTIONS 598 A-4 JACOBI AND GEGENBAUER
POLYNOMIALS 601 A-5 LAGUERRE AND ASSOCIATED LAGUERRE FUNCTIONS 605 A-6
HERMITE POLYNOMIALS AND WEBER-HERMITE FUNCTIONS 607 A-7 MITTAG LEFHER
FUNCTION 609 APPENDIX B TABLES OF INTEGRAL TRANSFORMS 611 B-L FOURIER
TRANSFORMS 611 B-2 FOURIER COSINE TRANSFORMS 615 B-3 FOURIER SINE
TRANSFORMS 617 B-4 LAPLACE TRANSFORMS 619 B-5 HANKEL TRANSFORMS 624 B-6
MELLIN TRANSFORMS 627 B-7 HUBERT TRANSFORMS 630 B-8 STIELTJES TRANSFORMS
633 B-9 FINITE FOURIER COSINE TRANSFORMS 636 B-10 FINITE FOURIER SINE
TRANSFORMS 638 B-LL FINITE LAPLACE TRANSFORMS 640 B-12 Z TRANSFORMS 642
B-13 FINITE HANKEL TRANSFORMS 644 ANSWERS AND HINTS TO SELECTED
EXERCISES 645 2.19 EXERCISES 645 3.9 EXERCISES 651 4.11 EXERCISES 655
6.8 EXERCISES 662 7.5 EXERCISES 662 8.8 EXERCISES 663 9.13 EXERCISES 664
10.6 EXERCISES 665 11.6 EXERCISES 667 12.8 EXERCISES 667 13.5 EXERCISES
670 16.5 EXERCISES 670 17.4 EXERCISES 670 18.9 EXERCISES 671 19.5
EXERCISES 671 BIBLIOGRAPHY 673 INDEX 689
|
| adam_txt |
INTEGRAL TRANSFORMS AND THEIR APPLICATIONS SECOND EDITION LOKENATH
DEBNATH DAMBARU BHATTA ^IJCHAPMAN & HALL/CRC M M TAYLOR & FRANCIS GROUP
BOCA RATON LONDON NEW YORK CHAPMAN & HALL/CRC IS AN IMPRINT OF THE
TAYLOR & FRANCIS GROUP, AN INFORMA BUSINESS CONTENTS 1 INTEGRAL
TRANSFORMS 1 1.1 BRIEF HISTORICAL INTRODUCTION 1 1.2 BASIC CONCEPTS AND
DEFINITIONS 6 2 FOURIER TRANSFORMS AND THEIR APPLICATIONS 9 2.1
INTRODUCTION 9 2.2 THE FOURIER INTEGRAL FORMULAS 10 2.3 DEFINITION OF
THE FOURIER TRANSFORM AND EXAMPLES 12 2.4 FOURIER TRANSFORMS OF
GENERALIZED FUNCTIONS 17 2.5 BASIC PROPERTIES OF FOURIER TRANSFORMS 28
2.6 POISSON'S SUMMATION FORMULA 37 2.7 THE SHANNON SAMPLING THEOREM 44
2.8 GIBBS' PHENOMENON 54 2.9 HEISENBERG'S UNCERTAINTY PRINCIPLE 57 2.10
APPLICATIONS OF FOURIER TRANSFORMS TO ORDINARY DIFFERENTIAL EQUATIONS 60
2.11 SOLUTIONS OF INTEGRAL EQUATIONS 65 2.12 SOLUTIONS OF PARTIAL
DIFFERENTIAL EQUATIONS 68 2.13 FOURIER COSINE AND SINE TRANSFORMS WITH
EXAMPLES 91 2.14 PROPERTIES OF FOURIER COSINE AND SINE TRANSFORMS 93
2.15 APPLICATIONS OF FOURIER COSINE AND SINE TRANSFORMS TO PARTIAL
DIFFERENTIAL EQUATIONS 96 2.16 EVALUATION OF DEFINITE INTEGRALS 100 2.17
APPLICATIONS OF FOURIER TRANSFORMS IN MATHEMATICAL STATISTICS 103 2.18
MULTIPLE FOURIER TRANSFORMS AND THEIR APPLICATIONS 109 2.19 EXERCISES
119 3 LAPLACE TRANSFORMS AND THEIR BASIC PROPERTIES 133 3.1 INTRODUCTION
133 3.2 DEFINITION OF THE LAPLACE TRANSFORM AND EXAMPLES 134 3.3
EXISTENCE CONDITIONS FOR THE LAPLACE TRANSFORM 139 3.4 BASIC PROPERTIES
OF LAPLACE TRANSFORMS 140 3.5 THE CONVOLUTION THEOREM AND PROPERTIES OF
CONVOLUTION . . 145 3.6 DIFFERENTIATION AND INTEGRATION OF LAPLACE
TRANSFORMS . 151 3.7 THE INVERSE LAPLACE TRANSFORM AND EXAMPLES 154
3.8 TAUBERIAN THEOREMS AND WATSON'S LEMMA 168 3.9 EXERCISES 173 4
APPLICATIONS OF LAPLACE TRANSFORMS 181 4.1 INTRODUCTION 181 4.2
SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS 182 4.3 PARTIAL
DIFFERENTIAL EQUATIONS, INITIAL AND BOUNDARY VALUE PROBLEMS 207 4.4
SOLUTIONS OF INTEGRAL EQUATIONS 222 4.5 SOLUTIONS OF BOUNDARY VALUE
PROBLEMS 225 4.6 EVALUATION OF DEFMITE INTEGRALS 228 4.7 SOLUTIONS OF
DIFFERENCE AND DIFFERENTIAL-DIFFERENCE EQUATIONS . 230 4.8 APPLICATIONS
OF THE JOINT LAPLACE AND FOURIER TRANSFORM . . . 237 4.9 SUMMATION OF
INFINITE SERIES 248 4.10 TRANSFER FUNCTION AND IMPULSE RESPONSE FUNCTION
OF A LINEAR SYSTEM 251 4.11 EXERCISES 256 5 FRACTIONAL CALCULUS AND ITS
APPLICATIONS 269 5.1 INTRODUCTION 269 5.2 HISTORICAL COMMENTS 270 5.3
FRACTIONAL DERIVATIVES AND INTEGRALS 272 5.4 APPLICATIONS OF FRACTIONAL
CALCULUS 279 5.5 EXERCISES 282 6 APPLICATIONS OF INTEGRAL TRANSFORMS TO
FRACTIONAL DIFFERENTIAL AND INTEGRAL EQUATIONS 283 6.1 INTRODUCTION 283
6.2 LAPLACE TRANSFORMS OF FRACTIONAL INTEGRALS AND FRACTIONAL
DERIVATIVES 284 6.3 FRACTIONAL ORDINARY DIFFERENTIAL EQUATIONS 287 6.4
FRACTIONAL INTEGRAL EQUATIONS 290 6.5 INITIAL VALUE PROBLEMS FOR
FRACTIONAL DIFFERENTIAL EQUATIONS . 295 6.6 GREEN'S FUNCTIONS OF
FRACTIONAL DIFFERENTIAL EQUATIONS . . . . 298 6.7 FRACTIONAL PARTIAL
DIFFERENTIAL EQUATIONS 299 6.8 EXERCISES 312 7 HANKEL TRANSFORMS AND
THEIR APPLICATIONS 315 7.1 INTRODUCTION 315 7.2 THE HANKEL TRANSFORM AND
EXAMPLES 316 7.3 OPERATIONAL PROPERTIES OF THE HANKEL TRANSFORM 319 7.4
APPLICATIONS OF HANKEL TRANSFORMS TO PARTIAL DIFFERENTIAL EQUATIONS 322
7.5 EXERCISES 331 8 MELLIN TRANSFORMS AND THEIR APPLICATIONS 339 8.1
INTRODUCTION 339 8.2 DEFINITION OF THE MELLIN TRANSFORM AND EXAMPLES 340
8.3 BASIC OPERATIONAL PROPERTIES OF MELLIN TRANSFORMS 343 8.4
APPLICATIONS OF MELLIN TRANSFORMS 349 8.5 MELLIN TRANSFORMS OF THE WEYL
FRACTIONAL INTEGRAL AND THE WEYL FRACTIONAL DERIVATIVE 353 8.6
APPLICATION OF MELLIN TRANSFORMS TO SUMMATION OF SERIES . . 358 8.7
GENERALIZED MELLIN TRANSFORMS 361 8.8 EXERCISES 365 9 HUBERT AND
STIELTJES TRANSFORMS 371 9.1 INTRODUCTION 371 9.2 DEFINITION OF THE
HUBERT TRANSFORM AND EXAMPLES 372 9.3 BASIC PROPERTIES OF HUBERT
TRANSFORMS 375 9.4 HUBERT TRANSFORMS IN THE COMPLEX PLANE 378 9.5
APPLICATIONS OF HUBERT TRANSFORMS 380 9.6 ASYMPTOTIC EXPANSIONS OF
ONE-SIDED HUBERT TRANSFORMS . . . 388 9.7 DEFINITION OF THE STIELTJES
TRANSFORM AND EXAMPLES 391 9.8 BASIC OPERATIONAL PROPERTIES OF STIELTJES
TRANSFORMS 394 9.9 INVERSION THEOREMS FOR STIELTJES TRANSFORMS 396 9.10
APPLICATIONS OF STIELTJES TRANSFORMS 399 9.11 THE GENERALIZED STIELTJES
TRANSFORM 401 9.12 BASIC PROPERTIES OF THE GENERALIZED STIELTJES
TRANSFORM . 403 9.13 EXERCISES 404 10 FINITE FOURIER SINE AND COSINE
TRANSFORMS 407 10.1 INTRODUCTION 407 10.2 DEFINITIONS OF THE FINITE
FOURIER SINE AND COSINE TRANSFORMS AND EXAMPLES 408 10.3 BASIC
PROPERTIES OF FINITE FOURIER SINE AND COSINE TRANSFORMS 410 10.4
APPLICATIONS OF FINITE FOURIER SINE AND COSINE TRANSFORMS . . 416 10.5
MULTIPLE FINITE FOURIER TRANSFORMS AND THEIR APPLICATIONS . 422 10.6
EXERCISES 425 11 FINITE LAPLACE TRANSFORMS 429 11.1 INTRODUCTION 429
11.2 DEFINITION OF THE FINITE LAPLACE TRANSFORM AND EXAMPLES . . 430
11.3 BASIC OPERATIONAL PROPERTIES OF THE FINITE LAPLACE TRANSFORM 436
11.4 APPLICATIONS OF FINITE LAPLACE TRANSFORMS 439 11.5 TAUBERIAN
THEOREMS 443 11.6 EXERCISES 443 12 Z TRANSFORMS 445 12.1 INTRODUCTION
445 12.2 DYNAMIC LINEAR SYSTEMS AND IMPULSE RESPONSE 445 12.3 DEFINITION
OF THE Z TRANSFORM AND EXAMPLES 449 12.4 BASIC OPERATIONAL PROPERTIES OF
Z TRANSFORMS 453 12.5 THE INVERSE Z TRANSFORM AND EXAMPLES 459 12.6
APPLICATIONS OF Z TRANSFORMS TO FINITE DIFFERENCE EQUATIONS . 463 12.7
SUMMATION OF INFINITE SERIES 466 12.8 EXERCISES 469 13 FINITE HANKEL
TRANSFORMS 473 13.1 INTRODUCTION 473 13.2 DEFINITION OF THE FINITE
HANKEL TRANSFORM AND EXAMPLES . . . 473 13.3 BASIC OPERATIONAL
PROPERTIES 476 13.4 APPLICATIONS OF FINITE HANKEL TRANSFORMS 476 13.5
EXERCISES 481 14 LEGENDRE TRANSFORMS 485 14.1 INTRODUCTION 485 14.2
DEFINITION OF THE LEGENDRE TRANSFORM AND EXAMPLES 486 14.3 BASIC
OPERATIONAL PROPERTIES OF LEGENDRE TRANSFORMS 489 14.4 APPLICATIONS OF
LEGENDRE TRANSFORMS TO BOUNDARY VALUE PROBLEMS 497 14.5 EXERCISES 498 15
JACOBI AND GEGENBAUER TRANSFORMS 501 15.1 INTRODUCTION 501 15.2
DEFINITION OF THE JACOBI TRANSFORM AND EXAMPLES 501 15.3 BASIC
OPERATIONAL PROPERTIES 504 15.4 APPLICATIONS OF JACOBI TRANSFORMS TO THE
GENERALIZED HEAT CONDUCTION PROBLEM 505 15.5 THE GEGENBAUER TRANSFORM
AND ITS BASIC OPERATIONAL PROPERTIES 507 15.6 APPLICATION OF THE
GEGENBAUER TRANSFORM 510 16 LAGUERRE TRANSFORMS 511 16.1 INTRODUCTION
511 16.2 DEFINITION OF THE LAGUERRE TRANSFORM AND EXAMPLES 511 16.3
BASIC OPERATIONAL PROPERTIES 516 16.4 APPLICATIONS OF LAGUERRE
TRANSFORMS 520 16.5 EXERCISES 523 17 HERMITE TRANSFER MS 525 17.1
INTRODUCTION 525 17.2 DEFINITION OF THE HERMITE TRANSFORM AND EXAMPLES
526 17.3 BASIC OPERATIONAL PROPERTIES 529 17.4 EXERCISES 538 18 THE
RADON TRANSFORM AND ITS APPLICATIONS 539 18.1 INTRODUCTION 539 18.2 THE
RADON TRANSFORM 541 18.3 PROPERTIES OF THE RADON TRANSFORM 545 18.4 THE
RADON TRANSFORM OF DERIVATIVES 550 18.5 DERIVATIVES OF THE RADON
TRANSFORM 551 18.6 CONVOLUTION THEOREM FOR THE RADON TRANSFORM 553 18.7
INVERSE OF THE RADON TRANSFORM AND THE PARSEVAL RELATION . . 554 18.8
APPLICATIONS OF THE RADON TRANSFORM 560 18.9 EXERCISES 561 19 WAVELETS
AND WAVELET TRANSFORMS 563 19.1 BRIEF HISTORICAL REMARKS 563 19.2
CONTINUOUS WAVELET TRANSFORMS 565 19.3 THE DISCRETE WAVELET TRANSFORM
573 19.4 EXAMPLES OF ORTHONORMAL WAVELETS 575 19.5 EXERCISES 584
APPENDIX A SOME SPECIAL FUNCTIONS AND THEIR PROPERTIES 587 A-L GAMMA,
BETA, AND ERROR FUNCTIONS 587 A-2 BESSEL AND AIRY FUNCTIONS 592 A-3
LEGENDRE AND ASSOCIATED LEGENDRE FUNCTIONS 598 A-4 JACOBI AND GEGENBAUER
POLYNOMIALS 601 A-5 LAGUERRE AND ASSOCIATED LAGUERRE FUNCTIONS 605 A-6
HERMITE POLYNOMIALS AND WEBER-HERMITE FUNCTIONS 607 A-7 MITTAG LEFHER
FUNCTION 609 APPENDIX B TABLES OF INTEGRAL TRANSFORMS 611 B-L FOURIER
TRANSFORMS 611 B-2 FOURIER COSINE TRANSFORMS 615 B-3 FOURIER SINE
TRANSFORMS 617 B-4 LAPLACE TRANSFORMS 619 B-5 HANKEL TRANSFORMS 624 B-6
MELLIN TRANSFORMS 627 B-7 HUBERT TRANSFORMS 630 B-8 STIELTJES TRANSFORMS
633 B-9 FINITE FOURIER COSINE TRANSFORMS 636 B-10 FINITE FOURIER SINE
TRANSFORMS 638 B-LL FINITE LAPLACE TRANSFORMS 640 B-12 Z TRANSFORMS 642
B-13 FINITE HANKEL TRANSFORMS 644 ANSWERS AND HINTS TO SELECTED
EXERCISES 645 2.19 EXERCISES 645 3.9 EXERCISES 651 4.11 EXERCISES 655
6.8 EXERCISES 662 7.5 EXERCISES 662 8.8 EXERCISES 663 9.13 EXERCISES 664
10.6 EXERCISES 665 11.6 EXERCISES 667 12.8 EXERCISES 667 13.5 EXERCISES
670 16.5 EXERCISES 670 17.4 EXERCISES 670 18.9 EXERCISES 671 19.5
EXERCISES 671 BIBLIOGRAPHY 673 INDEX 689 |
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| author | Debnath, Lokenath 1935- Bhatta, Dambaru |
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| classification_rvk | SK 450 |
| ctrlnum | (OCoLC)67384266 (DE-599)BVBBV021835178 |
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| dewey-sort | 3515 3723 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV021835178 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:58:27Z |
| indexdate | 2024-07-09T20:45:44Z |
| institution | BVB |
| isbn | 9781584885757 1584885750 |
| language | English |
| lccn | 2006045638 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015047117 |
| oclc_num | 67384266 |
| open_access_boolean | |
| owner | DE-703 DE-92 DE-824 |
| owner_facet | DE-703 DE-92 DE-824 |
| physical | 700 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| spelling | Debnath, Lokenath 1935- Verfasser (DE-588)115600663 aut Integral transforms and their applications Lokenath Debnath ; Dambaru Bhatta 2. ed. Boca Raton [u.a.] Chapman & Hall/CRC 2007 700 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Transformations intégrales Integral transforms Anwendung (DE-588)4196864-5 gnd rswk-swf Integraltransformation (DE-588)4027235-7 gnd rswk-swf Integraltransformation (DE-588)4027235-7 s Anwendung (DE-588)4196864-5 s DE-604 Bhatta, Dambaru Verfasser (DE-588)102169715X aut http://www.loc.gov/catdir/enhancements/fy0653/2006045638-d.html Publisher description GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015047117&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Debnath, Lokenath 1935- Bhatta, Dambaru Integral transforms and their applications Transformations intégrales Integral transforms Anwendung (DE-588)4196864-5 gnd Integraltransformation (DE-588)4027235-7 gnd |
| subject_GND | (DE-588)4196864-5 (DE-588)4027235-7 |
| title | Integral transforms and their applications |
| title_auth | Integral transforms and their applications |
| title_exact_search | Integral transforms and their applications |
| title_exact_search_txtP | Integral transforms and their applications |
| title_full | Integral transforms and their applications Lokenath Debnath ; Dambaru Bhatta |
| title_fullStr | Integral transforms and their applications Lokenath Debnath ; Dambaru Bhatta |
| title_full_unstemmed | Integral transforms and their applications Lokenath Debnath ; Dambaru Bhatta |
| title_short | Integral transforms and their applications |
| title_sort | integral transforms and their applications |
| topic | Transformations intégrales Integral transforms Anwendung (DE-588)4196864-5 gnd Integraltransformation (DE-588)4027235-7 gnd |
| topic_facet | Transformations intégrales Integral transforms Anwendung Integraltransformation |
| url | http://www.loc.gov/catdir/enhancements/fy0653/2006045638-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015047117&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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