Nonstandard asymptotic analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1987
|
| Series: | Lecture notes in mathematics
1249 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 187 S. |
| ISBN: | 3540177671 0387177671 |
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| 100 | 1 | |a Berg, Imme van den |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nonstandard asymptotic analysis |c Imme van den Berg |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1987 | |
| 300 | |a IX, 187 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1249 | |
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| 650 | 4 | |a Asymptotic expansions | |
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Record in the Search Index
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CONTENTS
page
PART I
Chapter I. Four examples of nonstandard reasoning in asymptotics.
1. The approximation of the number n\ — dt by the partial sums of 2
the expansion ]s ^q(~1) s!e .
2. Stirling's formula. 17
3. The expansion at infinity of the Besselfunctions. 22
4. The configuration of the Taylor-polynomials of the exponential 35
function.
5. Conclusion. 42
PART II
Chapter II. Asymptotic expressions for the remainders associated to
co 2n *° n n
expansions of type y_ c —r« £« c z and Z_ c n!z , where
v 3V ri«O n n! n*0 n n=0 n '
c /c -» c.
n+p n
1. Definitions and notations. Some basic properties. 46
2. The case c /c -» c. 54
n+p n
3. Generalizations. 66
Chapter III. Asymptotic expressions for the remainders associated to
expansions of type Jo cq nJ, Jo cnzn and ^ cnn!zn:
critical regions, uniform behaviour.
1. Summation to the nearly minimal term of divergent series of type 72
nSo cnn!£n- f
2. The approximation factor A near the convergence circle: 30
case where f is majorized.
3. The approximation factors A*, A and A when c /c - c+o(1/Vn). 33
b) to o) n+p n
4. Application: uniform behaviour of remainders of high order. 92
page
PART III
Chapter IV. External sets.
1. What is permanence? 107
2. Halos and galaxies. 109
3. Generalized galaxies and halos. 118
4. Convex external sets. 126
5. External equations. 136
Chapter V. Approximation lemma's.
1. Asymptotic approximations of integrals. 142
2. Asymptotic approximations of sums. 149
Chapter VI. Shadow expansions.
1. The Goze decomposition. 152
2. Scales. 155
3. Definition and fundamental properties of shadow expansions. 158
4. Shadow expansions and approximations. 168
5. Summation to the smallest term. 170
References. 177
Index/Lexicon. 181 |
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| indexdate | 2024-07-20T04:38:28Z |
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| isbn | 3540177671 0387177671 |
| language | English |
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| physical | IX, 187 S. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Berg, Imme van den Verfasser aut Nonstandard asymptotic analysis Imme van den Berg Berlin [u.a.] Springer 1987 IX, 187 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1249 Analyse mathématique non standard Développements asymptotiques Niet-standaardanalyse gtt Asymptotic expansions Nonstandard mathematical analysis Nonstandard-Analysis (DE-588)4137021-1 gnd rswk-swf Asymptotische Methode (DE-588)4287476-2 gnd rswk-swf Nonstandard-Analysis (DE-588)4137021-1 s Asymptotische Methode (DE-588)4287476-2 s DE-604 Lecture notes in mathematics 1249 (DE-604)BV000676446 1249 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000399687&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Berg, Imme van den Nonstandard asymptotic analysis Lecture notes in mathematics Analyse mathématique non standard Développements asymptotiques Niet-standaardanalyse gtt Asymptotic expansions Nonstandard mathematical analysis Nonstandard-Analysis (DE-588)4137021-1 gnd Asymptotische Methode (DE-588)4287476-2 gnd |
| subject_GND | (DE-588)4137021-1 (DE-588)4287476-2 |
| title | Nonstandard asymptotic analysis |
| title_auth | Nonstandard asymptotic analysis |
| title_exact_search | Nonstandard asymptotic analysis |
| title_full | Nonstandard asymptotic analysis Imme van den Berg |
| title_fullStr | Nonstandard asymptotic analysis Imme van den Berg |
| title_full_unstemmed | Nonstandard asymptotic analysis Imme van den Berg |
| title_short | Nonstandard asymptotic analysis |
| title_sort | nonstandard asymptotic analysis |
| topic | Analyse mathématique non standard Développements asymptotiques Niet-standaardanalyse gtt Asymptotic expansions Nonstandard mathematical analysis Nonstandard-Analysis (DE-588)4137021-1 gnd Asymptotische Methode (DE-588)4287476-2 gnd |
| topic_facet | Analyse mathématique non standard Développements asymptotiques Niet-standaardanalyse Asymptotic expansions Nonstandard mathematical analysis Nonstandard-Analysis Asymptotische Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000399687&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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