Bessel and related functions: mathematical operations with respect to the order
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
De Gruyter
2020
|
| Schriftenreihe: | De Gruyter STEM
|
| Schlagworte: | |
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MARC
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| 100 | 1 | |a Apelblat, Alexander |e Verfasser |0 (DE-588)1127068245 |4 aut | |
| 245 | 1 | 0 | |a Bessel and related functions |b mathematical operations with respect to the order |c Alexander Apelblat |
| 264 | 1 | |a Berlin |b De Gruyter |c 2020 | |
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a De Gruyter STEM | |
| 650 | 0 | 7 | |a Bessel-Funktionen |0 (DE-588)4069359-4 |2 gnd |9 rswk-swf |
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| 653 | |a Allgemein | ||
| 653 | |a Allgemein | ||
| 653 | |a MAT034000 | ||
| 653 | |a MAT007000: MAT007000 MATHEMATICS / Differential Equations / General | ||
| 653 | |a SCI040000: SCI040000 SCIENCE / Physics / Mathematical & Computational | ||
| 653 | |a PBK: Calculus & mathematical analysis | ||
| 653 | |a PBKJ: Differential calculus & equations | ||
| 653 | |a PHU: Mathematical physics | ||
| 653 | |a Bessel-Funktion | ||
| 653 | |a MAT034000 | ||
| 653 | |a 1620: Hardcover, Softcover / Mathematik | ||
| 689 | 0 | 0 | |a Bessel-Funktionen |0 (DE-588)4069359-4 |D s |
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| 710 | 2 | |a Walter de Gruyter GmbH & Co. KG |0 (DE-588)10095502-2 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-032186103 | ||
Datensatz im Suchindex
| _version_ | 1804181555134857216 |
|---|---|
| adam_text | CONTENTS
PREFACE
*
VII
1
INTRODUCTION
*
1
2
PROPERTIES
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
*
5
2.1
DEFINITIONS
AND
NOTATIONS
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
AND
ASSOCIATED
DIFFERENTIAL
EQUATIONS
*
5
2.2
INTERRELATIONS,
RECURRENCE
RELATIONS,
DIFFERENTIAL
AND
INTEGRAL
FORMULAS
FOR
THE
BESSEL
MZ)
AND
Y^Z)
AND
THE
HANKEL
H
V
(1)
(Z)
AND
H
V
(2)
(
Z
)
FUNCTIONS
-----
12
2.3
INTERRELATIONS,
RECURRENCE
RELATIONS,
DIFFERENTIAL
AND
INTEGRAL
FORMULAS
FOR
THE
MODIFIED
BESSEL
/
V
(Z)
AND
K^Z)
FUNCTIONS
*
14
2.4
INTERRELATIONS,
RECURRENCE
RELATIONS,
DIFFERENTIAL
AND
INTEGRAL
FORMULAS
FOR
THE
STRUVE
H^Z)
AND
THE
MODIFIED
STRUVE
ZJZ)
FUNCTIONS
-----
16
2.5
INTERRELATIONS,
RECURRENCE
RELATIONS
AND
DIFFERENTIAL
FORMULAS
FOR
THE
LOMMEL
S
PTV
(Z)
AND
S^
V
(Z)
FUNCTIONS
*
18
2.6
INTERRELATIONS,
RECURRENCE
RELATIONS,
DIFFERENTIAL
AND
INTEGRAL
FORMULAS
FOR
THE
ANGER
)^Z)
AND
THE
WEBER
E^Z)
FUNCTIONS
*
20
2.7
INTERRELATIONS,
RECURRENCE
RELATIONS,
DIFFERENTIAL
AND
INTEGRAL
FORMULAS
FOR
THE
KELVIN
BER^Z),
BEUZ),
THE
MODIFIED
KELVIN
KER^Z),
KEUZ)
AND
HER^Z),
HEMZ)
FUNCTIONS
*
21
2.8
INTERRELATIONS,
RECURRENCE
RELATIONS,
DIFFERENTIAL
AND
INTEGRAL
FORMULAS
FOR
THE
BESSEL
INTEGRAL
FUNCTIONS
*
22
2.9
SERIES
EXPANSIONS
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
*
23
2.10
BESSEL
AND
RELATED
FUNCTIONS
OF
HALF
ODD
INTEGER
ORDER
*
27
2.11
BESSEL
AND
RELATED
FUNCTIONS
EXPRESSED
IN
TERMS
OF
SPECIAL
FUNCTIONS
*
31
2.12
INTEGRAL
REPRESENTATION
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
*
33
2.13
DIFFERENTIAL
EQUATIONS
REDUCIBLE
TO
THE
BESSEL
DIFFERENTIAL
EQUATIONS
*
43
3
DIFFERENTIATION
AND
INTEGRATION
WITH
RESPECT
TO
THE
ORDER
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
*
78
3.1
FIRST
DERIVATIVES
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
WITH
RESPECT
TO
THE
ORDER
V:
UNRESTRICTED
VALUES
OF
THE
ORDER
V
*
78
3.2
FIRST
DERIVATIVES
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
WITH
RESPECT
TO
THE
ORDER
V:
PARTICULAR
VALUES
OF
THE
ORDER
V
*
86
3.3
DERIVATIVES
WITH
RESPECT
TO
THE
ORDER
V
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
BASED
ON
INTEGRAL
REPRESENTATIONS
*
101
XII
*
CONTENTS
3.4
HIGHER
ORDER
DERIVATIVES
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
WITH
RESPECT
TO
THE
ORDER
V
*
119
4
MATHEMATICAL
OPERATIONS
WITH
RESPECT
TO
THE
ORDER
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
-
INTEGRATION,
DIFFERENTIATION,
SERIES
AND
LIMITS
*
134
4.1
INTEGRATION
WITH
RESPECT
TO
THE
ORDER
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
-----
134
4.2
INTEGRATION
AND
DIFFERENTIATION
WITH
RESPECT
TO
THE
ORDER
OF
THE
BESSEL
FUNCTION
OF
THE
FIRST
KIND
BY
APPLYING
THE
LAPLACE
TRANSFORM
APPROACH
*
142
4.3
INTEGRATION
AND
DIFFERENTIATION
WITH
RESPECT
TO
THE
ORDER
OF
THE
MODIFIED
BESSEL
FUNCTION
OF
THE
FIRST
KIND
BY
APPLYING
THE
LAPLACE
TRANSFORM
APPROACH
*
154
4.4
DIFFERENTIATION
WITH
RESPECT
TO
THE
ORDER
OF
THE
ANGER
FUNCTION
AND
THE
WEBER
FUNCTION
BY
APPLYING
THE
LAPLACE
TRANSFORM
APPROACH
-----
162
4.5
INTEGRATION
AND
DIFFERENTIATION
WITH
RESPECT
TO
THE
ORDER
OF
THE
STRUVE
FUNCTIONS
BY
APPLYING
THE
LAPLACE
TRANSFORM
APPROACH
*
168
4.6
DIFFERENTIATION
WITH
RESPECT
TO
THE
ORDER
OF
THE
KELVIN
FUNCTIONS
BY
APPLYING
THE
LAPLACE
TRANSFORM
APPROACH
*
176
4.7
DIFFERENTIATION
WITH
RESPECT
TO
THE
ORDER
OF
THE
INTEGRAL
BESSEL
FUNCTIONS
BY
APPLYING
THE
LAPLACE
TRANSFORM
APPROACH
*
179
4.8
ZEROS
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
AS
A
FUNCTION
OF
THEIR
ORDER
-----
183
4.9
ZEROS
OF
THE
BESSEL
FUNCTIONS
WITH
RESPECT
TO
THE
ARGUMENT
AS
A
FUNCTION
OF
THEIR
ORDER
-----
193
4.10
BESSEL
FUNCTIONS
OF
EQUAL
OR
NEARLY
EQUAL
ORDER
AND
ARGUMENT
-----
211
4.11
THE
ASYMPTOTIC
LIMIT
OF
THE
BESSEL
FUNCTION
VJVTYX)
EXPRESSED
AS
THE
SHIFTED
DIRAC
FUNCTION
S(X
-1).
EVALUATION
OF
INTEGRAL
REPRESENTATIONS
OF
ELEMENTARY
FUNCTIONS,
SPECIAL
FUNCTIONS,
MATHEMATICAL
CONSTANTS,
INTEGRAL
TRANSFORMS,
ASYMPTOTIC
RELATIONS,
INTEGRALS
AND
LIMITS
OF
FUNCTIONAL
SERIES
*
216
REFERENCES
*
241
APPENDIX
A
THE
BESSEL
AND
RELATED
FUNCTIONS
INTEGRALS
*
249
APPENDIX
B
LIMITS
REPRESENTING
SPECIAL
FUNCTIONS
*
279
APPENDIX
C
NOTATION
AND
DEFINITIONS
OF
SPECIAL
FUNCTIONS
*
315
INDEX
*
321
|
| adam_txt |
CONTENTS
PREFACE
*
VII
1
INTRODUCTION
*
1
2
PROPERTIES
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
*
5
2.1
DEFINITIONS
AND
NOTATIONS
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
AND
ASSOCIATED
DIFFERENTIAL
EQUATIONS
*
5
2.2
INTERRELATIONS,
RECURRENCE
RELATIONS,
DIFFERENTIAL
AND
INTEGRAL
FORMULAS
FOR
THE
BESSEL
MZ)
AND
Y^Z)
AND
THE
HANKEL
H
V
(1)
(Z)
AND
H
V
(2)
(
Z
)
FUNCTIONS
-----
12
2.3
INTERRELATIONS,
RECURRENCE
RELATIONS,
DIFFERENTIAL
AND
INTEGRAL
FORMULAS
FOR
THE
MODIFIED
BESSEL
/
V
(Z)
AND
K^Z)
FUNCTIONS
*
14
2.4
INTERRELATIONS,
RECURRENCE
RELATIONS,
DIFFERENTIAL
AND
INTEGRAL
FORMULAS
FOR
THE
STRUVE
H^Z)
AND
THE
MODIFIED
STRUVE
ZJZ)
FUNCTIONS
-----
16
2.5
INTERRELATIONS,
RECURRENCE
RELATIONS
AND
DIFFERENTIAL
FORMULAS
FOR
THE
LOMMEL
S
PTV
(Z)
AND
S^
V
(Z)
FUNCTIONS
*
18
2.6
INTERRELATIONS,
RECURRENCE
RELATIONS,
DIFFERENTIAL
AND
INTEGRAL
FORMULAS
FOR
THE
ANGER
)^Z)
AND
THE
WEBER
E^Z)
FUNCTIONS
*
20
2.7
INTERRELATIONS,
RECURRENCE
RELATIONS,
DIFFERENTIAL
AND
INTEGRAL
FORMULAS
FOR
THE
KELVIN
BER^Z),
BEUZ),
THE
MODIFIED
KELVIN
KER^Z),
KEUZ)
AND
HER^Z),
HEMZ)
FUNCTIONS
*
21
2.8
INTERRELATIONS,
RECURRENCE
RELATIONS,
DIFFERENTIAL
AND
INTEGRAL
FORMULAS
FOR
THE
BESSEL
INTEGRAL
FUNCTIONS
*
22
2.9
SERIES
EXPANSIONS
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
*
23
2.10
BESSEL
AND
RELATED
FUNCTIONS
OF
HALF
ODD
INTEGER
ORDER
*
27
2.11
BESSEL
AND
RELATED
FUNCTIONS
EXPRESSED
IN
TERMS
OF
SPECIAL
FUNCTIONS
*
31
2.12
INTEGRAL
REPRESENTATION
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
*
33
2.13
DIFFERENTIAL
EQUATIONS
REDUCIBLE
TO
THE
BESSEL
DIFFERENTIAL
EQUATIONS
*
43
3
DIFFERENTIATION
AND
INTEGRATION
WITH
RESPECT
TO
THE
ORDER
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
*
78
3.1
FIRST
DERIVATIVES
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
WITH
RESPECT
TO
THE
ORDER
V:
UNRESTRICTED
VALUES
OF
THE
ORDER
V
*
78
3.2
FIRST
DERIVATIVES
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
WITH
RESPECT
TO
THE
ORDER
V:
PARTICULAR
VALUES
OF
THE
ORDER
V
*
86
3.3
DERIVATIVES
WITH
RESPECT
TO
THE
ORDER
V
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
BASED
ON
INTEGRAL
REPRESENTATIONS
*
101
XII
*
CONTENTS
3.4
HIGHER
ORDER
DERIVATIVES
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
WITH
RESPECT
TO
THE
ORDER
V
*
119
4
MATHEMATICAL
OPERATIONS
WITH
RESPECT
TO
THE
ORDER
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
-
INTEGRATION,
DIFFERENTIATION,
SERIES
AND
LIMITS
*
134
4.1
INTEGRATION
WITH
RESPECT
TO
THE
ORDER
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
-----
134
4.2
INTEGRATION
AND
DIFFERENTIATION
WITH
RESPECT
TO
THE
ORDER
OF
THE
BESSEL
FUNCTION
OF
THE
FIRST
KIND
BY
APPLYING
THE
LAPLACE
TRANSFORM
APPROACH
*
142
4.3
INTEGRATION
AND
DIFFERENTIATION
WITH
RESPECT
TO
THE
ORDER
OF
THE
MODIFIED
BESSEL
FUNCTION
OF
THE
FIRST
KIND
BY
APPLYING
THE
LAPLACE
TRANSFORM
APPROACH
*
154
4.4
DIFFERENTIATION
WITH
RESPECT
TO
THE
ORDER
OF
THE
ANGER
FUNCTION
AND
THE
WEBER
FUNCTION
BY
APPLYING
THE
LAPLACE
TRANSFORM
APPROACH
-----
162
4.5
INTEGRATION
AND
DIFFERENTIATION
WITH
RESPECT
TO
THE
ORDER
OF
THE
STRUVE
FUNCTIONS
BY
APPLYING
THE
LAPLACE
TRANSFORM
APPROACH
*
168
4.6
DIFFERENTIATION
WITH
RESPECT
TO
THE
ORDER
OF
THE
KELVIN
FUNCTIONS
BY
APPLYING
THE
LAPLACE
TRANSFORM
APPROACH
*
176
4.7
DIFFERENTIATION
WITH
RESPECT
TO
THE
ORDER
OF
THE
INTEGRAL
BESSEL
FUNCTIONS
BY
APPLYING
THE
LAPLACE
TRANSFORM
APPROACH
*
179
4.8
ZEROS
OF
THE
BESSEL
AND
RELATED
FUNCTIONS
AS
A
FUNCTION
OF
THEIR
ORDER
-----
183
4.9
ZEROS
OF
THE
BESSEL
FUNCTIONS
WITH
RESPECT
TO
THE
ARGUMENT
AS
A
FUNCTION
OF
THEIR
ORDER
-----
193
4.10
BESSEL
FUNCTIONS
OF
EQUAL
OR
NEARLY
EQUAL
ORDER
AND
ARGUMENT
-----
211
4.11
THE
ASYMPTOTIC
LIMIT
OF
THE
BESSEL
FUNCTION
VJVTYX)
EXPRESSED
AS
THE
SHIFTED
DIRAC
FUNCTION
S(X
-1).
EVALUATION
OF
INTEGRAL
REPRESENTATIONS
OF
ELEMENTARY
FUNCTIONS,
SPECIAL
FUNCTIONS,
MATHEMATICAL
CONSTANTS,
INTEGRAL
TRANSFORMS,
ASYMPTOTIC
RELATIONS,
INTEGRALS
AND
LIMITS
OF
FUNCTIONAL
SERIES
*
216
REFERENCES
*
241
APPENDIX
A
THE
BESSEL
AND
RELATED
FUNCTIONS
INTEGRALS
*
249
APPENDIX
B
LIMITS
REPRESENTING
SPECIAL
FUNCTIONS
*
279
APPENDIX
C
NOTATION
AND
DEFINITIONS
OF
SPECIAL
FUNCTIONS
*
315
INDEX
*
321 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Apelblat, Alexander |
| author_GND | (DE-588)1127068245 |
| author_facet | Apelblat, Alexander |
| author_role | aut |
| author_sort | Apelblat, Alexander |
| author_variant | a a aa |
| building | Verbundindex |
| bvnumber | BV046776818 |
| classification_rvk | SK 680 SK 500 SK 920 |
| ctrlnum | (DE-599)DNB1197408878 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV046776818 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T14:48:37Z |
| indexdate | 2024-07-10T08:53:31Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032186103 |
| open_access_boolean | |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter STEM |
| spelling | Apelblat, Alexander Verfasser (DE-588)1127068245 aut Bessel and related functions mathematical operations with respect to the order Alexander Apelblat Berlin De Gruyter 2020 txt rdacontent n rdamedia nc rdacarrier De Gruyter STEM Bessel-Funktionen (DE-588)4069359-4 gnd rswk-swf Paperback / softback Allgemein MAT034000 MAT007000: MAT007000 MATHEMATICS / Differential Equations / General SCI040000: SCI040000 SCIENCE / Physics / Mathematical & Computational PBK: Calculus & mathematical analysis PBKJ: Differential calculus & equations PHU: Mathematical physics Bessel-Funktion 1620: Hardcover, Softcover / Mathematik Bessel-Funktionen (DE-588)4069359-4 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032186103&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Apelblat, Alexander Bessel and related functions mathematical operations with respect to the order Bessel-Funktionen (DE-588)4069359-4 gnd |
| subject_GND | (DE-588)4069359-4 |
| title | Bessel and related functions mathematical operations with respect to the order |
| title_auth | Bessel and related functions mathematical operations with respect to the order |
| title_exact_search | Bessel and related functions mathematical operations with respect to the order |
| title_exact_search_txtP | Bessel and related functions mathematical operations with respect to the order |
| title_full | Bessel and related functions mathematical operations with respect to the order Alexander Apelblat |
| title_fullStr | Bessel and related functions mathematical operations with respect to the order Alexander Apelblat |
| title_full_unstemmed | Bessel and related functions mathematical operations with respect to the order Alexander Apelblat |
| title_short | Bessel and related functions |
| title_sort | bessel and related functions mathematical operations with respect to the order |
| title_sub | mathematical operations with respect to the order |
| topic | Bessel-Funktionen (DE-588)4069359-4 gnd |
| topic_facet | Bessel-Funktionen |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032186103&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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