Computation of special functions:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
John Wiley & Sons
1996
|
| Series: | A Wiley-Interscience Publication
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXVI, 717 Seiten graph. Darst. Diskette 9 cm |
| ISBN: | 0471119636 |
Staff View
MARC
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| 245 | 1 | 0 | |a Computation of special functions |c Shanjie Zhang, Department of Electronic Science and Engineering, Nanjing University, Nanjing, China, Jianming Jin, Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois |
| 264 | 1 | |a New York, NY [u.a.] |b John Wiley & Sons |c 1996 | |
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| 650 | 4 | |a Functions (Mathematics) | |
| 650 | 4 | |a Functions, Special |x Data processing | |
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Record in the Search Index
| _version_ | 1804125471451906048 |
|---|---|
| adam_text | CONTENTS
PREFACE xi
ACKNOWLEDGMENTS xvii
LIST OF COMPUTER PROGRAMS xix
1. BERNOULLI AND EULER NUMBERS 1
1.1 Bernoulli Numbers / 1
1.2 Euler Numbers / 6
1.3 Mathematical Table / 10
References / 11
2. ORTHOGONAL POLYNOMIALS 12
2.1 Introduction / 12
2.2 Chebyshev Polynomials / 13
2.3 Laguerre Polynomials / 18
2.4 Hermite Polynomials / 20
2.5 Numerical Computation / 23
2.6 Application in Numerical Integration / 27
References / 43
Hi
iV CONTENTS
3. GAMMA, BETA, AND PSI FUNCTIONS 44
3.1 Gamma Function / 44
3.2 Beta Function / 53
3.3 Psi Function / 55
3.4 Incomplete Gamma Function / 61
3.5 Incomplete Beta Function / 64
3.6 Mathematical Tables / 66
References and Further Reading / 76
4. LEGENDRE FUNCTIONS 77
4.1 Introduction / 77
4.2 Legendre Functions of the First Kind / 78
4.3 Legendre Functions of the Second Kind / 83
4.4 Associated Legendre Functions of the First Kind / 89
4.5 Associated Legendre Functions of the Second Kind / 96
4.6 Legendre Functions with an Arbitrary Degree / 104
4.7 Mathematical Tables / 113
References and Further Reading / 125
5. BESSEL FUNCTIONS 126
5.1 Introduction / 126
5.2 Computation of J0(x), Jx{x), Y0(x), and Yx(x) I 131
5.3 Computation of Jn(x) and Yn(x) with Real
Arguments / 140
5.4 Computation of Yn(z) and Yn(z) with Complex
Arguments / 149
5.5 Computation of Jv(z) and Jv(z) with an Arbitrary
Order / 161
5.6 Assessment of Validity and Accuracy of
Computation / 175
5.7 Zeros of Bessel Functions / 180
5.8 Lambda Functions / 182
5.9 Mathematical Tables / 184
References and Further Reading / 201
6. MODIFIED BESSEL FUNCTIONS 202
6.1 Introduction / 202
6.2 Computation of I0(x), /,(*), K0(x), and #,(*) / 207
CONTENTS V
6.3 Computation of /„(*) and Kn(x) with Real
Arguments / 213
6.4 Computation of In(z) and Kn(z) with Complex
Arguments / 217
6.5 Computation of I£z) and Kv{z) with an Arbitrary
Order / 225
6.6 Computation of H(J z) and Hf z) for Complex
Arguments / 235
6.7 Mathematical Tables / 239
References and Further Reading / 251
7. INTEGRALS OF BESSEL FUNCTIONS 252
7.1 Simple Integrals of Bessel Functions / 252
7.2 Simple Integrals of Modified Bessel Functions / 261
7.3 Curves and Tables / 268
References / 272
8. SPHERICAL BESSEL FUNCTIONS 273
8.1 Spherical Bessel Functions / 273
8.2 Riccati Bessel Functions / 283
8.3 Modified Spherical Bessel Functions / 286
8.4 Mathematical Tables / 295
References and Further Reading / 306
9. KELVIN FUNCTIONS 307
9.1 Introduction / 307
9.2 Mathematical Properties / 311
9.3 Asymptotic Expansions / 312
9.4 Numerical Computation / 315
9.5 Zeros of Kelvin Functions / 321
9.6 Mathematical Tables / 321
Reference / 324
10. AIRY FUNCTIONS 325
10.1 Introduction / 325
10.2 Numerical Computation / 329
10.3 Mathematical Tables / 336
References / 340
VI CONTENTS
11. STRUVE FUNCTIONS 341
11.1 Struve Functions / 341
11.2 Modified Struve Functions / 353
11.3 Mathematical Tables / 362
References / 365
12. HYPERGEOMETRIC AND CONFLUENT
HYPERGEOMETRIC FUNCTIONS 366
12.1 Definition of Hypergeometric Functions / 366
12.2 Properties of Hypergeometric Functions / 368
12.3 Linear Transformation Formulas / 369
12.4 Recurrence Relations for Hypergeometric
Functions / 372
12.5 Special Functions Expressed as Hypergeometric
Functions / 373
12.6 Numerical Computation of Hypergeometric
Functions / 374
12.7 Definition of Confluent Hypergeometric
Functions / 385
12.8 Properties of Confluent Hypergeometric
Functions / 387
12.9 Recurrence Relations for Confluent Hypergeometric
Functions / 389
12.10 Special Functions Expressed as Confluent
Hypergeometric Functions / 394
12.11 Definition of Whittaker Functions / 395
12.12 Numerical Computation of Confluent Hypergeometric
Functions / 398
12.13 Mathematical Tables / 411
References and Further Reading / 424
13. PARABOLIC CYLINDER FUNCTIONS 425
13.1. Introduction / 425
13.2 Definitions of Parabolic Cylinder Functions / 428
13.3 Basic Properties / 432
13.4 Series and Asymptotic Expansions / 437
13.5 Numerical Computation / 438
13.6 Mathematical Tables / 455
References and Further Reading / 474
CONTENTS Vii
14. MATHIEU FUNCTIONS 475
14.1 Definition of Mathieu Functions / 475
14.2 Determination of Expansion Coefficients and
Characteristic Values / 477
14.3 Approximate Calculation of Characteristic Values / 482
14.4 Expansion of Mathieu Functions When q 1 / 485
14.5 Properties of Mathieu Functions / 487
14.6 Definition of Modified Mathieu Functions / 489
14.7 Properties of Modified Mathieu Functions / 496
14.8 Numerical Computation: Algorithms and Computer
Programs / 501
14.9 Mathematical Tables / 520
References and Further Reading / 535
15. SPHEROIDAL WAVE FUNCTIONS 536
15.1 Spheroidal Coordinate Systems / 536
15.2 Wave Equation and Its Solution in Spheroidal
Coordinates / 540
15.3 Definitions of Angular and Radial Prolate Spheroidal
Wave Functions / 542
15.4 Determination of Characteristic Values and Expansion
Coefficients / 550
15.5 Evaluation of Prolate Radial Wave Functions of the
Second Kind for Small c$ / 556
15.6 Definitions of Angular and Radial Oblate Spheroidal
Wave Functions / 559
15.7 Evaluation of Oblate Radial Wave Functions of the
Second Kind for Small c£ / 567
15.8 Numerical Computation: Algorithms and Computer
Programs / 569
15.9 Mathematical Tables / 594
References / 619
16. ERROR FUNCTION AND FRESNEL INTEGRALS 620
16.1 Introduction to Error Function / 620
16.2 Numerical Computation of Error Function / 621
16.3 Gaussian Probability Integral / 624
16.4 Introduction to Fresnel Integrals / 625
16.5 Series and Asymptotic Expansions of Fresnel
Integrals / 629
VHi CONTENTS
16.6 Numerical Computation of Fresnel Integrals / 630
16.7 Zeros of Error Function and Fresnel Integrals / 635
16.8 Mathematical Tables / 636
References and Further Reading / 643
17. COSINE AND SINE INTEGRALS 644
17.1 Introduction / 644
17.2 Series and Asymptotic Expansions / 646
17.3 Numerical Computation / 647
17.4 Mathematical Table / 651
References and Further Readings / 653
18. ELLIPTIC INTEGRALS AND JACOBIAN ELLIPTIC
FUNCTIONS 654
18.1 Introduction to Elliptic Integrals / 654
18.2 Series Expansion of Elliptic Integrals / 659
18.3 Numerical Computation of Elliptic Integrals / 661
18.4 Introduction to Jacobian Elliptic Functions / 666
18.5 Numerical Computation of Jacobian Elliptic
Functions / 670
18.6 Mathematical Tables / 672
References and Further Reading / 679
19. EXPONENTIAL INTEGRALS 680
19.1 Introduction / 680
19.2 Series, Asymptotic, and Continued Fraction
Expressions / 682
19.3 Rational Approximations / 683
19.4 Numerical Computation / 684
19.5 Mathematical Tables / 688
References / 693
20. SUMMARY OF METHODS FOR COMPUTING SPECIAL
FUNCTIONS 694
APPENDIX A DERIVATION OF SOME SPECIAL
DIFFERENTIAL EQUATIONS 697
A. 1 Helmholtz Equation and Separation of Variables / 697
A.2 Circular Cylindrical Coordinates / 698
A.3 Elliptic Cylindrical Coordinates / 700
CONTENTS ix
A.4 Parabolic Cylindrical Coordinates / 700
A.5 Spherical Coordinates / 701
A.6 Prolate Spheroidal Coordinates / 701
A.7 Oblate Spheroidal Coordinates / 702
A.8 Parabolic Coordinates / 703
References / 703
APPENDIX B ROOT FINDING METHODS 704
B.I Newton s Method / 704
B.2 Modified Newton s Method / 706
B.3 Secant Method / 706
Reference / 706
APPENDIX C ABOUT THE SOFTWARE 707
INDEX 709
INDEX OF COMPUTER PROGRAMS 715
|
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| author | Zhang, Shanjie Jin, Jian-Ming 1962- |
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| author_facet | Zhang, Shanjie Jin, Jian-Ming 1962- |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-09T18:02:05Z |
| institution | BVB |
| isbn | 0471119636 |
| language | English |
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| physical | XXVI, 717 Seiten graph. Darst. Diskette 9 cm |
| publishDate | 1996 |
| publishDateSearch | 1996 |
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| publisher | John Wiley & Sons |
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| series2 | A Wiley-Interscience Publication |
| spelling | Zhang, Shanjie Verfasser (DE-588)1067913017 aut Computation of special functions Shanjie Zhang, Department of Electronic Science and Engineering, Nanjing University, Nanjing, China, Jianming Jin, Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois New York, NY [u.a.] John Wiley & Sons 1996 XXVI, 717 Seiten graph. Darst. Diskette 9 cm txt rdacontent n rdamedia nc rdacarrier A Wiley-Interscience Publication Datenverarbeitung Functions (Mathematics) Functions, Special Data processing Spezielle Funktion (DE-588)4182213-4 gnd rswk-swf Spezielle Funktion (DE-588)4182213-4 s DE-604 Jin, Jian-Ming 1962- Verfasser (DE-588)137256159 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007349924&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zhang, Shanjie Jin, Jian-Ming 1962- Computation of special functions Datenverarbeitung Functions (Mathematics) Functions, Special Data processing Spezielle Funktion (DE-588)4182213-4 gnd |
| subject_GND | (DE-588)4182213-4 |
| title | Computation of special functions |
| title_auth | Computation of special functions |
| title_exact_search | Computation of special functions |
| title_full | Computation of special functions Shanjie Zhang, Department of Electronic Science and Engineering, Nanjing University, Nanjing, China, Jianming Jin, Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois |
| title_fullStr | Computation of special functions Shanjie Zhang, Department of Electronic Science and Engineering, Nanjing University, Nanjing, China, Jianming Jin, Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois |
| title_full_unstemmed | Computation of special functions Shanjie Zhang, Department of Electronic Science and Engineering, Nanjing University, Nanjing, China, Jianming Jin, Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois |
| title_short | Computation of special functions |
| title_sort | computation of special functions |
| topic | Datenverarbeitung Functions (Mathematics) Functions, Special Data processing Spezielle Funktion (DE-588)4182213-4 gnd |
| topic_facet | Datenverarbeitung Functions (Mathematics) Functions, Special Data processing Spezielle Funktion |
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