Handbook of elliptic integrals for engineers and scientists:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1971
|
| Ausgabe: | 2. ed., rev. |
| Schriftenreihe: | Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen
67 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 358 S. graph. Darst. |
| ISBN: | 3540053182 0387053182 |
Internformat
MARC
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| 100 | 1 | |a Byrd, Paul F. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Handbook of elliptic integrals for engineers and scientists |c Paul F. Byrd ; Morris D. Friedmann |
| 250 | |a 2. ed., rev. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1971 | |
| 300 | |a 358 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804136091901493248 |
|---|---|
| adam_text | Table of Contents.
Page
Preface to the First Edition VII
Preface to the Second Edition IX
List of Symbols and Abbreviations XIV
Introduction 1
Definitions and Fundamental Relations 8
110. Elliptic Integrals 8
Definitions, p. 8. — Legendre s relation, p. 10. — Special values, p. 10. —
Limiting values, p. 11. — Extension of the range of p and k, p. 12. —
Addition formulas p. 13. — Special addition formulas, p. 13 — Differen¬
tial equations, p. 15. — Sketches of E(q , k), F( p, A), E{k) and K(k),
p. 16. — Conformal Mappings, p. 17.
120. Jacobian Elliptic Functions 18
Definitions, p. 18. — Fundamental relations, p. 20. — Special values,
p. 20. — Addition formulas, p. 23. — Double and half arguments,
p. 24. — Complex and imaginary arguments, p. 24. — Relation to
Theta functions, p. 24. — Approximation formulas, p. 24. — Dif¬
ferential equations, p. 25. — Identities, p. 25. — Sketches, p. 26. —
Conformal Mappings, p. 28. — Applications, p. 28.
130. Jacobi s Inverse Elliptic Functions 29
Definitions, p. 29. — Identities, p. 31. — Special values, p. 31. —
Addition formulas, p. 32. — Special addition formulas, p. 32.
140. Jacobian Zeta Function 33
Definitions, p. 33. — Special values, p. 33. —! Maximum value, p. 34. —
Limiting value, p. 34. — Approximation formula, p. 34. — Addition
formulas, p. 34. — Special addition formula, p. 34. — Complex and
imaginary arguments, p. 34. — Relation to Theta functions, p. 34. —
Sketches, p. 35.
ISO. Heuman s Lambda Function 35
Definitions, p. 35. — Special values, p. 36. — Limiting value, p. 36. —
Addition formula, p. 36. — Special addition formulas, p. 36. —
Relation to Theta functions, p. 37. — Sketches, p. 37.
160. Transformation Formulas for Elliptic Functions and Elliptic Integrals 38
Imaginary modulus transformation, p. 38. — Imaginary argument
transformation, p. 38. — Reciprocal modulus transformation, p. 38. —
Landen s transformation, p. 39. — Gauss transformation, p. 39. —
Other transformations, p. 40.
Reduction of Algebraic Integrands to Jacobian Elliptic Functions 42
200. Introduction 42
210. Integrands Involving Square Roots of Sums and Differences of Squares 43
Introduction, p. 43. — Table of Integrals, p. 45.
XII Table of Contents.
Page
230. Integrands Involving the Square root of a Cubic 65
Introduction p. 65 — Table of Integrals p. 68.
250. Integrands Involving the Square root of a Quartic 95
Introduction p. 95. — Table of Integrals p. 98.
270. Integrands Involving Miscellaneous Fractional Powers of Polynomials 148
Reduction of Trigonometric Integrands to Jacobian Elliptic Functions . . . .162
Reduction of Hyperbolic Integrands to Jacobian Elliptic Functions 182
Tables of Integrals of Jacobian Elliptic Functions 191
310. Recurrence Formulas for the Integrals of the Twelve Jacobian Elliptic
Functions 191
330. Additional Recurrence Formulas 198
360. Integrands Involving Various Combinations of Jacobian Elliptic
Functions 211
390. Integrals of Jacobian Inverse Elliptic Functions 221
Elliptic Integrals of the Third Kind 223
400. Introduction 223
410. Table of Integrals 224
Complete integrals, p. 225. — Incomplete integrals, p. 232.
Table of Miscellaneous Elliptic Integrals Involving Trigonometric or Hyperbolic
Integrands 240
510. Single Integrals 240
530. Multiple Integrals 245
Elliptic Integrals Resulting from Laplace Transformations 249
Hyperelliptic Integrals 252
575. Introduction 252
576. Table of Integrals 256
Integrals of the Elliptic Integrals 272
610. With Respect to the Modulus 272
630. With Respect to the Argument 276
Derivatives 282
710. With Respect to the Modulus 282
Differentiation of the elliptic integrals, p. 282. — Differentiation of
the Jacobian elliptic functions, p. 283.
730. With Respect to the Argument 284
Differentiation of the elliptic integrals, p. 284. — Differentiation of
the Jacobian elliptic functions, p. 284. — Differentiation of the
Jacobian inverse functions, p. 285
733. With Respect to the Parameter 286
Differentiation of the normal elliptic integral of the third kind, p. 286.—
Differentiation of other elliptic integrals, p. 287.
Table of Contents. XIII
Page
Miscellaneous Integrals and Formulas 288
Expansions in Series 298
900. Developments of the Elliptic Integrals 298
Complete elliptic integrals of the first and second kind, p. 298 — The
nome, p. 300. — Incomplete elliptic integrals of the first and second
kind, p. 300. — Heuman s function, p. 301. — Jacobian Zeta function,
p. 301. — The elliptic integral of the third kind, p. 302.
907. Developments of Jacobian Elliptic Functions 303
Maclaurin s series, p. 303. — Fourier series, p. 304. — Infinite products,
P 306 — Other developments, p. 307.
Appendix 308
1030. Weierstrassian Elliptic Functions and Elliptic Integrals 308
Definition, p. 308. — Relation to Jacobian elliptic functions, p. 309. —
Fundamental relations, p. 309. — Derivatives, p. 309. — Special
values, p. 310. — Addition formulas, p. 310. — Relation to Theta
functions, p. 310.—Weierstrassian normal elliptic integrals, p. 311.—
Other integrals, p. 312. — Illustrative example, p. 313.
1050. Theta Functions 315
Definitions, p. 315. — Special values, p. 316. — Quasi Addition For¬
mulas, p. 317. — Differential equation, p. 317. — Relation to Jacobian
elliptic functions, p. 318. — Relation to elliptic integrals, p. 318.
1060. Pseudo elliptic Integrals 320
Definition, p. 320. — Examples, p. 321.
Table of Numerical Values 322
Values of the complete elliptic integrals K and E. and of the nome q
with respect to the modular angle, p. 323. — Values of the complete
elliptic integrals K, K , E, E , and of the nomes q and q with respect
to A2, p. 324. — Values of the incomplete elliptic integral of the first
kind, F( p, k), p. 325. — Values of the incomplete elliptic integral of
the second kind, E( p. A), p. 331. — Values of the Function KZ(fi, A),
p. 337 — Values of Heuman s function A^ifi, A), p. 345
Bibliography 351
Supplementary Bibliography 353
In *ex 355
|
| adam_txt |
Table of Contents.
Page
Preface to the First Edition VII
Preface to the Second Edition IX
List of Symbols and Abbreviations XIV
Introduction 1
Definitions and Fundamental Relations 8
110. Elliptic Integrals 8
Definitions, p. 8. — Legendre's relation, p. 10. — Special values, p. 10. —
Limiting values, p. 11. — Extension of the range of p and k, p. 12. —
Addition formulas p. 13. — Special addition formulas, p. 13 — Differen¬
tial equations, p. 15. — Sketches of E(q , k), F( p, A), E{k) and K(k),
p. 16. — Conformal Mappings, p. 17.
120. Jacobian Elliptic Functions 18
Definitions, p. 18. — Fundamental relations, p. 20. — Special values,
p. 20. — Addition formulas, p. 23. — Double and half arguments,
p. 24. — Complex and imaginary arguments, p. 24. — Relation to
Theta functions, p. 24. — Approximation formulas, p. 24. — Dif¬
ferential equations, p. 25. — Identities, p. 25. — Sketches, p. 26. —
Conformal Mappings, p. 28. — Applications, p. 28.
130. Jacobi's Inverse Elliptic Functions 29
Definitions, p. 29. — Identities, p. 31. — Special values, p. 31. —
Addition formulas, p. 32. — Special addition formulas, p. 32.
140. Jacobian Zeta Function 33
Definitions, p. 33. — Special values, p. 33. —! Maximum value, p. 34. —
Limiting value, p. 34. — Approximation formula, p. 34. — Addition
formulas, p. 34. — Special addition formula, p. 34. — Complex and
imaginary arguments, p. 34. — Relation to Theta functions, p. 34. —
Sketches, p. 35.
ISO. Heuman's Lambda Function 35
Definitions, p. 35. — Special values, p. 36. — Limiting value, p. 36. —
Addition formula, p. 36. — Special addition formulas, p. 36. —
Relation to Theta functions, p. 37. — Sketches, p. 37.
160. Transformation Formulas for Elliptic Functions and Elliptic Integrals 38
Imaginary modulus transformation, p. 38. — Imaginary argument
transformation, p. 38. — Reciprocal modulus transformation, p. 38. —
Landen's transformation, p. 39. — Gauss' transformation, p. 39. —
Other transformations, p. 40.
Reduction of Algebraic Integrands to Jacobian Elliptic Functions 42
200. Introduction 42
210. Integrands Involving Square Roots of Sums and Differences of Squares 43
Introduction, p. 43. — Table of Integrals, p. 45.
XII Table of Contents.
Page
230. Integrands Involving the Square root of a Cubic 65
Introduction p. 65 — Table of Integrals p. 68.
250. Integrands Involving the Square root of a Quartic 95
Introduction p. 95. — Table of Integrals p. 98.
270. Integrands Involving Miscellaneous Fractional Powers of Polynomials 148
Reduction of Trigonometric Integrands to Jacobian Elliptic Functions . . . .162
Reduction of Hyperbolic Integrands to Jacobian Elliptic Functions 182
Tables of Integrals of Jacobian Elliptic Functions 191
310. Recurrence Formulas for the Integrals of the Twelve Jacobian Elliptic
Functions 191
330. Additional Recurrence Formulas 198
360. Integrands Involving Various Combinations of Jacobian Elliptic
Functions 211
390. Integrals of Jacobian Inverse Elliptic Functions 221
Elliptic Integrals of the Third Kind 223
400. Introduction 223
410. Table of Integrals 224
Complete integrals, p. 225. — Incomplete integrals, p. 232.
Table of Miscellaneous Elliptic Integrals Involving Trigonometric or Hyperbolic
Integrands 240
510. Single Integrals 240
530. Multiple Integrals 245
Elliptic Integrals Resulting from Laplace Transformations 249
Hyperelliptic Integrals 252
575. Introduction 252
576. Table of Integrals 256
Integrals of the Elliptic Integrals 272
610. With Respect to the Modulus 272
630. With Respect to the Argument 276
Derivatives 282
710. With Respect to the Modulus 282
Differentiation of the elliptic integrals, p. 282. — Differentiation of
the Jacobian elliptic functions, p. 283.
730. With Respect to the Argument 284
Differentiation of the elliptic integrals, p. 284. — Differentiation of
the Jacobian elliptic functions, p. 284. — Differentiation of the
Jacobian inverse functions, p. 285
733. With Respect to the Parameter 286
Differentiation of the normal elliptic integral of the third kind, p. 286.—
Differentiation of other elliptic integrals, p. 287.
Table of Contents. XIII
Page
Miscellaneous Integrals and Formulas 288
Expansions in Series 298
900. Developments of the Elliptic Integrals 298
Complete elliptic integrals of the first and second kind, p. 298 — The
nome, p. 300. — Incomplete elliptic integrals of the first and second
kind, p. 300. — Heuman's function, p. 301. — Jacobian Zeta function,
p. 301. — The elliptic integral of the third kind, p. 302.
907. Developments of Jacobian Elliptic Functions 303
Maclaurin's series, p. 303. — Fourier series, p. 304. — Infinite products,
P 306 — Other developments, p. 307.
Appendix 308
1030. Weierstrassian Elliptic Functions and Elliptic Integrals 308
Definition, p. 308. — Relation to Jacobian elliptic functions, p. 309. —
Fundamental relations, p. 309. — Derivatives, p. 309. — Special
values, p. 310. — Addition formulas, p. 310. — Relation to Theta
functions, p. 310.—Weierstrassian normal elliptic integrals, p. 311.—
Other integrals, p. 312. — Illustrative example, p. 313.
1050. Theta Functions 315
Definitions, p. 315. — Special values, p. 316. — Quasi Addition For¬
mulas, p. 317. — Differential equation, p. 317. — Relation to Jacobian
elliptic functions, p. 318. — Relation to elliptic integrals, p. 318.
1060. Pseudo elliptic Integrals 320
Definition, p. 320. — Examples, p. 321.
Table of Numerical Values 322
Values of the complete elliptic integrals K and E. and of the nome q
with respect to the modular angle, p. 323. — Values of the complete
elliptic integrals K, K', E, E', and of the nomes q and q' with respect
to A2, p. 324. — Values of the incomplete elliptic integral of the first
kind, F( p, k), p. 325. — Values of the incomplete elliptic integral of
the second kind, E( p. A), p. 331. — Values of the Function KZ(fi, A),
p. 337 — Values of Heuman's function A^ifi, A), p. 345
Bibliography 351
Supplementary Bibliography 353
In *ex 355 |
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| author | Byrd, Paul F. Friedman, Morris David |
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| building | Verbundindex |
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| callnumber-first | Q - Science |
| callnumber-label | QA343 |
| callnumber-raw | QA343 |
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| callnumber-sort | QA 3343 |
| callnumber-subject | QA - Mathematics |
| ctrlnum | (OCoLC)142349 (DE-599)BVBBV022118347 |
| dewey-full | 515/.983/0212 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.983/0212 |
| dewey-search | 515/.983/0212 |
| dewey-sort | 3515 3983 3212 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed., rev. |
| format | Book |
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| genre | 1\p (DE-588)4155008-0 Formelsammlung gnd-content |
| genre_facet | Formelsammlung |
| id | DE-604.BV022118347 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:16:06Z |
| indexdate | 2024-07-09T20:50:54Z |
| institution | BVB |
| isbn | 3540053182 0387053182 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015333213 |
| oclc_num | 142349 |
| open_access_boolean | |
| owner | DE-706 DE-83 |
| owner_facet | DE-706 DE-83 |
| physical | 358 S. graph. Darst. |
| psigel | TUB-nvmb |
| publishDate | 1971 |
| publishDateSearch | 1971 |
| publishDateSort | 1971 |
| publisher | Springer |
| record_format | marc |
| series | Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen |
| series2 | Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen |
| spelling | Byrd, Paul F. Verfasser aut Handbook of elliptic integrals for engineers and scientists Paul F. Byrd ; Morris D. Friedmann 2. ed., rev. Berlin [u.a.] Springer 1971 358 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen 67 Fonctions elliptiques Elliptic functions Elliptisches Integral (DE-588)4152029-4 gnd rswk-swf Tabelle (DE-588)4184303-4 gnd rswk-swf Integralrechnung (DE-588)4027232-1 gnd rswk-swf Formel (DE-588)4133595-8 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf 1\p (DE-588)4155008-0 Formelsammlung gnd-content Integralrechnung (DE-588)4027232-1 s DE-604 Elliptisches Integral (DE-588)4152029-4 s Formel (DE-588)4133595-8 s 2\p DE-604 Tabelle (DE-588)4184303-4 s 3\p DE-604 Mathematik (DE-588)4037944-9 s 4\p DE-604 Friedman, Morris David Verfasser (DE-588)1114683787 aut Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen 67 (DE-604)BV000000395 67 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015333213&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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Byrd, Paul F. Friedman, Morris David Handbook of elliptic integrals for engineers and scientists Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen Fonctions elliptiques Elliptic functions Elliptisches Integral (DE-588)4152029-4 gnd Tabelle (DE-588)4184303-4 gnd Integralrechnung (DE-588)4027232-1 gnd Formel (DE-588)4133595-8 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4152029-4 (DE-588)4184303-4 (DE-588)4027232-1 (DE-588)4133595-8 (DE-588)4037944-9 (DE-588)4155008-0 |
| title | Handbook of elliptic integrals for engineers and scientists |
| title_auth | Handbook of elliptic integrals for engineers and scientists |
| title_exact_search | Handbook of elliptic integrals for engineers and scientists |
| title_exact_search_txtP | Handbook of elliptic integrals for engineers and scientists |
| title_full | Handbook of elliptic integrals for engineers and scientists Paul F. Byrd ; Morris D. Friedmann |
| title_fullStr | Handbook of elliptic integrals for engineers and scientists Paul F. Byrd ; Morris D. Friedmann |
| title_full_unstemmed | Handbook of elliptic integrals for engineers and scientists Paul F. Byrd ; Morris D. Friedmann |
| title_short | Handbook of elliptic integrals for engineers and scientists |
| title_sort | handbook of elliptic integrals for engineers and scientists |
| topic | Fonctions elliptiques Elliptic functions Elliptisches Integral (DE-588)4152029-4 gnd Tabelle (DE-588)4184303-4 gnd Integralrechnung (DE-588)4027232-1 gnd Formel (DE-588)4133595-8 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Fonctions elliptiques Elliptic functions Elliptisches Integral Tabelle Integralrechnung Formel Mathematik Formelsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015333213&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT byrdpaulf handbookofellipticintegralsforengineersandscientists AT friedmanmorrisdavid handbookofellipticintegralsforengineersandscientists |