Integrals and sums: Some new formulae for their numerical evaluation
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Athlone
1970
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 88 S. |
| ISBN: | 0485111144 |
Internformat
MARC
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| 100 | 1 | |a Chakravarti, P. C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Integrals and sums |b Some new formulae for their numerical evaluation |
| 264 | 1 | |a London |b Athlone |c 1970 | |
| 300 | |a X, 88 S. | ||
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| 650 | 4 | |a Intégrales | |
| 650 | 7 | |a Intégrales |2 ram | |
| 650 | 4 | |a Intégration numérique | |
| 650 | 7 | |a Intégration numérique |2 ram | |
| 650 | 4 | |a Integrals | |
| 650 | 4 | |a Numerical integration | |
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Datensatz im Suchindex
| _version_ | 1804122430000594944 |
|---|---|
| adam_text | CONTENTS
I. COMPLEX VARIABLE METHOD 1
Introduction, 1
1. The complex error lemma, 2
2. The general rectangular formula with prescribed weighting functions, 4
3. le /^ da;, 7
4. The weighting functions cosh {ax), sinh (ax), cos (fix) and sin (fix), 10
5. The Fourier coefficients, 12
6. sin(fix)/x.f(x)dx, 12
Jo
7. fX (z *o)°*/(z)d*. 14
8. f*V ^ (a;,, *)«•/(*) dx, 15
Jxo
II. THE C POLYNOMIALS AND THE D FUNCTIONS 17
Introduction, 17
1. The C polynomials, 18
2. Some applications, 21
3. The functions Dr(z, q), 23
4. Formulae for the calculation of C,(z, q) and Dr(z, q), 24
5. Upper bounds for | eM Dr(s, q) | and e Cr(s, q) |, 27
6. An asymptotic formula for Dr(0, q), 30
7. The general rectangular formula with the exponential weighting
function, 31
8. Error bounds for the formulae of Sections 3 and 4 of Chapter I, 33
9. Error estimates for the formulae with the exponential and allied
weighting functions, comparison with other formulae, and numerical
examples, 35
10. Formulae for the summation of series with exponential and allied
weighting functions, 41
11. Error bounds for the formulae of Section 10, 43
III. OPERATIONAL METHOD 46
Introduction, 46
1. The general rectangular error operator, 46
2. The general rectangular formula with arbitrary correction points, 48
3. The general rectangular formula with the exponential weighting
function, 50
4. The weighting function (x — xo)°; 50
5. The weighting function e 1I(a; r0)o«, 52
X CONTENTS
IV. ARBITRARY CORRECTION POINT FORMULAE AND
FORMULAE WITH CORRECTION TERMS EXPRESSED
IN TERMS OF QUANTITIES OTHER THAN DERIVA¬
TIVES 54
Introduction, 54
1. The derivation of arbitrary correction point formulae: (i) Complex
variable method, 54
2. (ii) Operational method, 56
3. (iii) The method of integration by parts, 56
4. The general rectangular formula with arbitrary correction points for
the unit weighting function, 57
5. The derivation of formulae with correction terms expressed in terms
of quantities other than derivatives, 58
6. Operational method: The general rectangular formula with forward
and/or backward difference correction, 60
7. The forward and backward difference formulae for the exponential
and allied weighting functions, 62
8. The central difference formulae for the exponential and allied weight¬
ing functions, 64
9. Numerical examples, 69
10. The forward, backward and central difference formulae for
X (x x0)« (xn x) nf(x) dx, 71
APPENDICES 73
A. A METHOD BASED ON THE PROPERTIES OF THE FUNCTION
®(z,H,v) 73
B. A PROBLEM OF UNST7MMABLE DIVERGENCE 76
C. TABLES 78
Description of the tables and usage, 78
Table I Ao( ± u) = D0(0, ± u) +£ and A,.( ± u) = Dr(0, + u),
r = 1 (1) 11, u = 0 (0.02) 1; 8 figures, 79
Table II ,( + iv) = D0(0, + iv) + $ and A,( + iv) = Z r(0, ± iv),
r = 1 (1) 11, v = 0 (0.02) 1; 8 figures, 83
Table III £{ (r + a)}, WT(a) Ur(a) and Vr(a), r = 0 (1) 8, a = ± f,
± f, ± h ±h ± i; £ to 8 figures, others to 8 decimals, 87
REFERENCES 89
|
| any_adam_object | 1 |
| author | Chakravarti, P. C. |
| author_facet | Chakravarti, P. C. |
| author_role | aut |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-raw | 519.4 517/.6 |
| dewey-search | 519.4 517/.6 |
| dewey-sort | 3519.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV008064355 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:13:45Z |
| institution | BVB |
| isbn | 0485111144 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005306952 |
| oclc_num | 100765 |
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| owner_facet | DE-20 DE-824 DE-29T DE-91 DE-BY-TUM |
| physical | X, 88 S. |
| publishDate | 1970 |
| publishDateSearch | 1970 |
| publishDateSort | 1970 |
| publisher | Athlone |
| record_format | marc |
| spelling | Chakravarti, P. C. Verfasser aut Integrals and sums Some new formulae for their numerical evaluation London Athlone 1970 X, 88 S. txt rdacontent n rdamedia nc rdacarrier Intégrales Intégrales ram Intégration numérique Intégration numérique ram Integrals Numerical integration Integration Mathematik (DE-588)4072852-3 gnd rswk-swf Numerische Integration (DE-588)4172168-8 gnd rswk-swf Integration Mathematik (DE-588)4072852-3 s DE-604 Numerische Integration (DE-588)4172168-8 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005306952&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chakravarti, P. C. Integrals and sums Some new formulae for their numerical evaluation Intégrales Intégrales ram Intégration numérique Intégration numérique ram Integrals Numerical integration Integration Mathematik (DE-588)4072852-3 gnd Numerische Integration (DE-588)4172168-8 gnd |
| subject_GND | (DE-588)4072852-3 (DE-588)4172168-8 |
| title | Integrals and sums Some new formulae for their numerical evaluation |
| title_auth | Integrals and sums Some new formulae for their numerical evaluation |
| title_exact_search | Integrals and sums Some new formulae for their numerical evaluation |
| title_full | Integrals and sums Some new formulae for their numerical evaluation |
| title_fullStr | Integrals and sums Some new formulae for their numerical evaluation |
| title_full_unstemmed | Integrals and sums Some new formulae for their numerical evaluation |
| title_short | Integrals and sums |
| title_sort | integrals and sums some new formulae for their numerical evaluation |
| title_sub | Some new formulae for their numerical evaluation |
| topic | Intégrales Intégrales ram Intégration numérique Intégration numérique ram Integrals Numerical integration Integration Mathematik (DE-588)4072852-3 gnd Numerische Integration (DE-588)4172168-8 gnd |
| topic_facet | Intégrales Intégration numérique Integrals Numerical integration Integration Mathematik Numerische Integration |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005306952&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT chakravartipc integralsandsumssomenewformulaefortheirnumericalevaluation |