Holdings: Symbolic asymptotics

Symbolic asymptotics:

Saved in:

Bibliographic Details
Main Author:	Shackell, John R. 1943- (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2004
Series:	Algorithms and computation in mathematics 12
Subjects:	Algorithms Asymptotic expansions Computeralgebra Asymptotik Reelle Funktion
Online Access:	Inhaltsverzeichnis
Item Description:	Literaturverz. S. 235-240
Physical Description:	XI, 243 S. graph. Darst. 24 cm
ISBN:	3540210970

Staff View

MARC


LEADER	00000nam a2200000 cb4500
001	BV019615771
003	DE-604
005	20141218
007	t
008	041201s2004 gw d\|\|\| \|\|\|\| 00\|\|\| eng d
015			\|a 04,N10,0736 \|2 dnb
015			\|a 04,A36,0624 \|2 dnb
016	7		\|a 970130171 \|2 DE-101
020			\|a 3540210970 \|9 3-540-21097-0
024	3		\|a 9783540210979
035			\|a (OCoLC)54611207
035			\|a (DE-599)BVBBV019615771
040			\|a DE-604 \|b ger \|e rakddb
041	0		\|a eng
044			\|a gw \|c XA-DE-BE
049			\|a DE-91G \|a DE-384 \|a DE-634 \|a DE-11 \|a DE-188 \|a DE-19
050		0	\|a QA297
082	0		\|a 511/.4 \|2 22
084			\|a SK 470 \|0 (DE-625)143241: \|2 rvk
084			\|a MAT 260f \|2 stub
084			\|a MAT 418f \|2 stub
084			\|a 510 \|2 sdnb
084			\|a DAT 702f \|2 stub
100	1		\|a Shackell, John R. \|d 1943- \|e Verfasser \|0 (DE-588)129213977 \|4 aut
245	1	0	\|a Symbolic asymptotics \|c John R. Shackell
264		1	\|a Berlin [u.a.] \|b Springer \|c 2004
300			\|a XI, 243 S. \|b graph. Darst. \|c 24 cm
336			\|b txt \|2 rdacontent
337			\|b n \|2 rdamedia
338			\|b nc \|2 rdacarrier
490	1		\|a Algorithms and computation in mathematics \|v 12
500			\|a Literaturverz. S. 235-240
650		4	\|a Algorithms
650		4	\|a Asymptotic expansions
650	0	7	\|a Computeralgebra \|0 (DE-588)4010449-7 \|2 gnd \|9 rswk-swf
650	0	7	\|a Asymptotik \|0 (DE-588)4126634-1 \|2 gnd \|9 rswk-swf
650	0	7	\|a Reelle Funktion \|0 (DE-588)4048918-8 \|2 gnd \|9 rswk-swf
689	0	0	\|a Reelle Funktion \|0 (DE-588)4048918-8 \|D s
689	0	1	\|a Asymptotik \|0 (DE-588)4126634-1 \|D s
689	0	2	\|a Computeralgebra \|0 (DE-588)4010449-7 \|D s
689	0		\|5 DE-604
830		0	\|a Algorithms and computation in mathematics \|v 12 \|w (DE-604)BV011131286 \|9 12
856	4	2	\|m HEBIS Datenaustausch Darmstadt \|q application/pdf \|u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012945274&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA \|3 Inhaltsverzeichnis
999			\|a oai:aleph.bib-bvb.de:BVB01-012945274

Record in the Search Index

_version_	1804132977411620864
adam_text	JOHN R. SHACKELL SYMBOLIC ASYMPTOTICS SPRINGER CONTENTS INTRODUCTION 1 ZERO EQUIVALENCE 7 2.1 ZERO-EQUIVALENCE OF CONSTANTS 8 2.1.1 RICHARDSON S UNIFORMITY CONJECTURE 11 2.2 ZERO-EQUIVALENCE OF FUNCTIONS 13 2.2.1 EXAMPLES 22 2.2.2 THE SETS SI 25 2.3 MODULAR METHODS IN ZERO EQUIVALENCE 27 2.3.1 HENSEL LIFTING 28 2.3.2 EXAMPLES 30 2.4 GROWTH IN DEGREES 31 2.4.1 CANONICAL FORMS 32 2.5 SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS 33 2.5.1 NOTATION 33 2.5.2 RADICAL DIFFERENTIAL IDEALS 35 2.5.3 COMPUTING CHARACTERISTIC SETS 36 2.5.4 THE ROSENFELD-GROBNER ALGORITHM 36 2.5.5 CONSEQUENCES, APPLICATIONS 38 2.5.6 ZERO EQUIVALENCE 39 2.6 FINDING SYMMETRIES 39 HARDY FIELDS 43 3.1 DEFINITIONS AND EXAMPLES . 43 3.2 BUILDING HARDY FIELDS 45 3.3 ROUGH COMPARISONS 50 3.4 THE MAP 72 54 OUTPUT DATA STRUCTURES 59 4.1 ASYMPTOTIC POWER SERIES 59 4.2 MULTISERIES 61 X CONTENTS 4.3 OPERATIONS ON MULTISERIES 63 4.3.1 SUBSTITUTING INTO A POWER SERIES 65 4.3.2 THE LOGARITHM OF A MULTISERIES 68 4.3.3 THE EXPONENTIAL OF A MULTISERIES 69 4.3.4 POWERS OF A MULTISERIES 69 4.3.5 AMALGAMATING SCALES 70 4.3.6 SUBSTITUTING ONE MULTISERIES INTO ANOTHER 70 4.4 NESTED EXPANSIONS 71 4.4.1 COMPARISON OF NESTED FORMS 74 4.4.2 OPERATIONS ON NESTED FORMS AND EXPANSIONS 76 4.5 THE ALGEBRA OF STAR PRODUCTS 78 4.5.1 DEFINITIONS AND ELEMENTARY PROPERTIES 78 4.5.2 DIFFERENTIATION AND STAR PRODUCTS 81 ALGORITHMS FOR FUNCTION TOWERS 83 5.1 THE EXP-LOG ALGORITHM 84 5.1.1 CASE 1: /; = LOG H, H E FI-I 85 5.1.2 CASE 2: F T = EXPH, H E TI- 86 5.1.3 HANDLING DENOMINATORS AND OTHER POWERS 87 5.1.4 SUMMARY OF THE ALGORITHM 88 5.1.5 EXAMPLES 88 5.2 ASYMPTOTIC FIELDS 92 5.2.1 ADDING EXPONENTIALS 100 5.2.2 ADDING INTEGRALS 101 5.2.3 ALGEBRAIC EQUATIONS 110 5.3 COMPOSITIONS WITH MEROMORPHIC FUNCTIONS 116 5.4 CARTESIAN REPRESENTATIONS 125 ALGEBRAIC DIFFERENTIAL EQUATIONS 129 6.1 NESTED FORMS OF HARDY-FIELD SOLUTIONS 130 6.1.1 EXAMPLES 140 6.2 THE NUMBER OF CASES 144 6.3 REDUCING THE COMPLEXITY 150 6.3.1 A THEOREM FOR SPARSE DIFFERENTIAL EQUATIONS 151 INVERSE FUNCTIONS 155 7.1 INVERTING A NESTED EXPANSION 156 7.1.1 SUMMARY OF THE ALGORITHM FOR INVERSION 161 7.1.2 EXAMPLE 161 7.2 MULTISERIES OF INVERSE FUNCTIONS 163 7.2.1 PROOF OF THE ITERATION FORMULA 169 7.2.2 ASYMPTOTIC FIELDS AND INVERSE FUNCTIONS 173 CONTENTS XI IMPLICIT FUNCTIONS 175 8.1 A SPECIAL CASE 176 8.1.1 COMPUTATION AND CHECKING OF CANDIDATES 177 8.1.2 EXAMPLES 178 8.2 SYSTEMS OF EXP-LOG EQUATIONS 179 8.2.1 ZERO EQUIVALENCE 180 8.2.2 SKETCH OF THE METHOD 180 8.2.3 BUILDING ESTIMATES FROM THE TOWER OF FIELDS 182 8.2.4 EXTENSION BY A LOGARITHM 182 8.2.5 EXTENSION BY AN EXPONENTIAL 183 8.2.6 OBTAINING THE NESTED FORMS 184 8.2.7 EXAMPLE 1 185 8.2.8 EXAMPLE 2 187 8.2.9 EXAMPLE 3 189 STAR*PRODUCT EXPANSIONS 191 9.1 EXP-LOG EXPANSIONS 191 9.1.1 REWRITING EXP-LOG EXPRESSIONS INTO STANDARD STAR EXPANSION FORM 193 9.1.2 ORDER COMPARISONS 196 9.2 GROWTH CLASSES IN HARDY FIELDS 201 9.2.1 GENERALIZING THE 7 N S 201 9.3 GENERALIZED STAR PRODUCTS 204 9.3.1 EXPANSIONS 207 9.3.2 NON-INTEGRAL ITERATES AND MULTIPLE SCALES 208 9.4 REAL ITERATES OF INCREASING FUNCTIONS 209 OSCILLATING FUNCTIONS 215 10.1 AN INTERVAL CALCULUS ALGORITHM 216 10.1.1 OUR CALCULUS OF INTERVALS 217 10.2 LIM-SUPS AND LIM-INFS 220 10.3 WANDERING FUNCTIONS 224 10.4 WANDERING EXPANSIONS 231 REFERENCES 235 INDEX 241
any_adam_object	1
author	Shackell, John R. 1943-
author_GND	(DE-588)129213977
author_facet	Shackell, John R. 1943-
author_role	aut
author_sort	Shackell, John R. 1943-
author_variant	j r s jr jrs
building	Verbundindex
bvnumber	BV019615771
callnumber-first	Q - Science
callnumber-label	QA297
callnumber-raw	QA297
callnumber-search	QA297
callnumber-sort	QA 3297
callnumber-subject	QA - Mathematics
classification_rvk	SK 470
classification_tum	MAT 260f MAT 418f DAT 702f
ctrlnum	(OCoLC)54611207 (DE-599)BVBBV019615771
dewey-full	511/.4
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	511 - General principles of mathematics
dewey-raw	511/.4
dewey-search	511/.4
dewey-sort	3511 14
dewey-tens	510 - Mathematics
discipline	Informatik Mathematik
format	Book
fullrecord	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02023nam a2200553 cb4500</leader><controlfield tag="001">BV019615771</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20141218 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">041201s2004 gw d\|\|\| \|\|\|\| 00\|\|\| eng d</controlfield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">04,N10,0736</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">04,A36,0624</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">970130171</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540210970</subfield><subfield code="9">3-540-21097-0</subfield></datafield><datafield tag="024" ind1="3" ind2=" "><subfield code="a">9783540210979</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)54611207</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV019615771</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">XA-DE-BE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-19</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA297</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511/.4</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 470</subfield><subfield code="0">(DE-625)143241:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 260f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 418f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">510</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">DAT 702f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Shackell, John R.</subfield><subfield code="d">1943-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)129213977</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Symbolic asymptotics</subfield><subfield code="c">John R. Shackell</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2004</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XI, 243 S.</subfield><subfield code="b">graph. Darst.</subfield><subfield code="c">24 cm</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Algorithms and computation in mathematics</subfield><subfield code="v">12</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverz. S. 235-240</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algorithms</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Asymptotic expansions</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Computeralgebra</subfield><subfield code="0">(DE-588)4010449-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Asymptotik</subfield><subfield code="0">(DE-588)4126634-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Reelle Funktion</subfield><subfield code="0">(DE-588)4048918-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Reelle Funktion</subfield><subfield code="0">(DE-588)4048918-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Asymptotik</subfield><subfield code="0">(DE-588)4126634-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Computeralgebra</subfield><subfield code="0">(DE-588)4010449-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Algorithms and computation in mathematics</subfield><subfield code="v">12</subfield><subfield code="w">(DE-604)BV011131286</subfield><subfield code="9">12</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HEBIS Datenaustausch Darmstadt</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012945274&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-012945274</subfield></datafield></record></collection>
id	DE-604.BV019615771
illustrated	Illustrated
indexdate	2024-07-09T20:01:23Z
institution	BVB
isbn	3540210970
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-012945274
oclc_num	54611207
open_access_boolean
owner	DE-91G DE-BY-TUM DE-384 DE-634 DE-11 DE-188 DE-19 DE-BY-UBM
owner_facet	DE-91G DE-BY-TUM DE-384 DE-634 DE-11 DE-188 DE-19 DE-BY-UBM
physical	XI, 243 S. graph. Darst. 24 cm
publishDate	2004
publishDateSearch	2004
publishDateSort	2004
publisher	Springer
record_format	marc
series	Algorithms and computation in mathematics
series2	Algorithms and computation in mathematics
spelling	Shackell, John R. 1943- Verfasser (DE-588)129213977 aut Symbolic asymptotics John R. Shackell Berlin [u.a.] Springer 2004 XI, 243 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Algorithms and computation in mathematics 12 Literaturverz. S. 235-240 Algorithms Asymptotic expansions Computeralgebra (DE-588)4010449-7 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Reelle Funktion (DE-588)4048918-8 gnd rswk-swf Reelle Funktion (DE-588)4048918-8 s Asymptotik (DE-588)4126634-1 s Computeralgebra (DE-588)4010449-7 s DE-604 Algorithms and computation in mathematics 12 (DE-604)BV011131286 12 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012945274&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Shackell, John R. 1943- Symbolic asymptotics Algorithms and computation in mathematics Algorithms Asymptotic expansions Computeralgebra (DE-588)4010449-7 gnd Asymptotik (DE-588)4126634-1 gnd Reelle Funktion (DE-588)4048918-8 gnd
subject_GND	(DE-588)4010449-7 (DE-588)4126634-1 (DE-588)4048918-8
title	Symbolic asymptotics
title_auth	Symbolic asymptotics
title_exact_search	Symbolic asymptotics
title_full	Symbolic asymptotics John R. Shackell
title_fullStr	Symbolic asymptotics John R. Shackell
title_full_unstemmed	Symbolic asymptotics John R. Shackell
title_short	Symbolic asymptotics
title_sort	symbolic asymptotics
topic	Algorithms Asymptotic expansions Computeralgebra (DE-588)4010449-7 gnd Asymptotik (DE-588)4126634-1 gnd Reelle Funktion (DE-588)4048918-8 gnd
topic_facet	Algorithms Asymptotic expansions Computeralgebra Asymptotik Reelle Funktion
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012945274&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV011131286
work_keys_str_mv	AT shackelljohnr symbolicasymptotics

Holdings

There is no print copy available.

Interlibrary loan Place Request Caution: Not in THWS collection! Indexes

MARC

Record in the Search Index

There is no print copy available.

Similar Items