Polynomial sequences: basic methods, special classes, and computational applications
Gespeichert in:
| Hauptverfasser: | , , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston
De Gruyter
[2024]
|
| Schriftenreihe: | De Gruyter studies in mathematics
Volume 96 |
| Schlagworte: | |
| Online-Zugang: | https://www.degruyter.com/isbn/9783110757231 Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | XVII, 506 Seiten Illustrationen 17 cm x 24 cm, 991 g |
| ISBN: | 9783110757231 3110757230 |
Internformat
MARC
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| 007 | t | ||
| 008 | 240118s2024 gw a||| |||| 00||| eng d | ||
| 015 | |a 23,N33 |2 dnb | ||
| 016 | 7 | |a 1299123546 |2 DE-101 | |
| 020 | |a 9783110757231 |c Festeinband : EUR 159.95 (DE) (freier Preis), EUR 159.95 (AT) (freier Preis) |9 978-3-11-075723-1 | ||
| 020 | |a 3110757230 |9 3-11-075723-0 | ||
| 024 | 3 | |a 9783110757231 | |
| 035 | |a (OCoLC)1417339894 | ||
| 035 | |a (DE-599)DNB1299123546 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c XA-DE-BE | ||
| 049 | |a DE-29T | ||
| 084 | |8 1\p |a 510 |2 23sdnb | ||
| 100 | 1 | |a Costabile, Francesco |e Verfasser |0 (DE-588)173968651 |4 aut | |
| 245 | 1 | 0 | |a Polynomial sequences |b basic methods, special classes, and computational applications |c Francesco Aldo Costabile, Maria Italia Gualtieri, Anna Napoli |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2024] | |
| 300 | |a XVII, 506 Seiten |b Illustrationen |c 17 cm x 24 cm, 991 g | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter studies in mathematics |v Volume 96 | |
| 653 | |a Polynomsequenzen | ||
| 653 | |a Numerische Analyse | ||
| 653 | |a Infinitesimalrechnung | ||
| 653 | |a echte Funktionen | ||
| 653 | |a Polynomsequenzen; Numerische Analysis; Infinitesimalrechnung; Reelle Funktionen | ||
| 653 | |a Polynomial sequences; Numerical Analysis; Infinitesimal calculus; Real-valued function | ||
| 700 | 1 | |a Gualtieri, Maria Italia |d 1962- |e Verfasser |0 (DE-588)1323198237 |4 aut | |
| 700 | 1 | |a Napoli, Anna |d 1969- |e Verfasser |0 (DE-588)1321451636 |4 aut | |
| 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, PDF |z 978-3-11-075724-8 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, EPUB |z 978-3-11-075732-3 |
| 830 | 0 | |a De Gruyter studies in mathematics |v Volume 96 |w (DE-604)BV000005407 |9 96 | |
| 856 | 4 | 2 | |m X:MVB |u https://www.degruyter.com/isbn/9783110757231 |
| 856 | 4 | 2 | |m B:DE-101 |q application/pdf |u https://d-nb.info/1299123546/04 |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034852059&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 883 | 1 | |8 1\p |a vlb |d 20230812 |q DE-101 |u https://d-nb.info/provenance/plan#vlb | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-034852059 | |
Datensatz im Suchindex
| _version_ | 1810467138750644224 |
|---|---|
| adam_text |
CONTENTS
PREFACE
-
VII
PARTL:
BASIC
METHODS
INTRODUCTION
-
3
0
0.1
0.1.1
0.2
0.3
INFINITE
LOWER
TRIANGULAR
MATRICES
AND
FORMAL
POWER
SERIES
-
5
DEFINITIONS
AND
FIRST
PROPERTIES
-
5
HESSENBERG
DETERMINANTS
-
7
TRIANGULAR
TOEPLITZ
MATRICES
-
11
A
CLASS
OF
TRIDIAGONAL
MATRICES
AND
THE
RELATED
DETERMINANT
COMPUTATION
-
13
0.4
0.5
0.6
FORMAL
POWER
SERIES:
ALGEBRAIC
STRUCTURE
-
17
THE
^-SERIES
AND
COMPOSITIONAL
INVERSE
-
19
FORMAL
POWER
SERIES
WITH
ONLY
EVEN
POWERS
AND
RELATED
TOEPLITZ
MATRICES
-
25
0.7
0.8
0.9
0.9.1
0.9.2
0.9.3
0.10
0.11
APPELL-TYPE
MATRICES
-
26
SHEFFER-TYPE
MATRICES
-
34
LIDSTONE-TYPE
MATRICES
-
40
ODD
LIDSTONE-TYPE
MATRICES
-
40
EVEN
LIDSTONE-TYPE
MATRICES
-
44
RELATIONSHIP
BETWEEN
APPELL-TYPE
AND
LIDSTONE-TYPE
MATRICES
-
47
PRODUCTION
OR
STIELTJES
MATRIX
-
47
HANKEL
MATRICES
-
49
1
POLYNOMIAL
SEQUENCES:
ALGEBRAIC
STRUCTURE,
RECURRENCE
AND
DETERMINANT
FORM,
OPERATIONAL
METHODS
-
56
1.1
1.2
1.3
1.4
1.5
1.5.1
1.5.2
1.6
1.7
1.8
1.9
1.10
THE
LINEAR
SPACE
P
-
56
RECURRENCE
RELATIONS
-
59
DETERMINANT
FORMS
-
62
BASIS,
CONNECTION
CONSTANTS
AND
CONDITION
NUMBER
-
66
ILLUSTRATIVE
EXAMPLES
-
68
FIBONACCI
POLYNOMIAL
SEQUENCES
-
71
CHEBYSHEV
POLYNOMIAL
SEQUENCES
OF
THE
FIRST
KIND
-
78
COMPARISON
BETWEEN
CONDITION
NUMBERS
-
86
OPERATIONAL
MATRICES
-
88
DERIVATION
MATRIX:
CALCULATION
-
88
INTEGRATION
MATRIX:
CALCULATION
-
90
ILLUSTRATIVE
EXAMPLES
-
92
XII
-
CONTENTS
2
2.1
2.2
2.3
2.4
2.5
2.6
2.6.1
2.6.2
2.6.3
SYMMETRIC
POLYNOMIAL
SEQUENCES
-
97
DEFINITIONS
-
97
MATRIX
FORM
-
98
THE
ALGEBRAIC
STRUCTURE
-
99
RECURRENCE
RELATIONS
-
100
DETERMINANT
FORMS
-
102
ILLUSTRATIVE
EXAMPLES
-
105
ODD
AND
EVEN
FIBONACCI
POLYNOMIAL
SEQUENCES
-
105
ODD
AND
EVEN
CHEBYSHEV
POLYNOMIAL
SEQUENCES
OF
THE
FIRST
KIND
-
109
ODD
AND
EVEN
CENTRAL
FACTORIAL
POLYNOMIAL
SEQUENCES
-
113
3
3.1
3.2
3.3
3.4
GENERATING
FUNCTIONS
-
117
DEFINITIONS
-
117
SERIES
MANIPULATION
-
118
THE
FACTORIAL
FUNCTION
AND
THE
GENERALIZED
HYPERGEOMETRIC
FUNCTIONS
-
119
OBTAINING
GENERATING
FUNCTIONS
BY
REPRESENTATION
IN
MONOMIAL
POWER
-
121
4
4.1
4.2
DIFFERENTIAL
OPERATOR
AND
SHEFFER
CLASSIFICATION
-
129
THE
POLYNOMIAL
SET
ASSOCIATED
WITH
A
POLYNOMIAL
SEQUENCE
-
129
DIFFERENTIAL
OPERATOR
ASSOCIATED
WITH
POLYNOMIAL
SEQUENCE:
SHEFFER
'
S
CLASSIFICATION
-
131
4.3
4.3.1
4.3.2
4.3.3
4.3.4
4.4
4.4.1
4.4.2
4.4.3
ILLUSTRATIVE
EXAMPLES
-
133
MONIC
LAGUERRE
POLYNOMIALS
-
133
LAGUERRE
POLYNOMIALS
-
134
HERMITE
POLYNOMIALS
-
135
APPELL
POLYNOMIAL
SEQUENCES
-
135
APPELL-TYPE
1
POLYNOMIAL
SEQUENCES
-
136
MATRIX
FORM
-
138
RECURRENCE
RELATIONS
AND
DETERMINANT
FORMS
-
139
PARTICULAR
CASES
-
140
5
5.1
5.2
5.3
THE
MONOMIALITY
PRINCIPLE
-
143
INTRODUCTION
-
143
THE
DERIVATIVE
AND
MULTIPLICATIVE
OPERATORS
-
144
ILLUSTRATIVE
EXAMPLES
-
146
CONTENTS
-
XIII
PART
II:
SPECIAL
CLASSES
OF
POLYNOMIAL
SEQUENCES
INTRODUCTION
-
155
6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10
6.11
6.11.1
6.11.2
6.11.3
6.11.4
6.11.5
SHEFFER
POLYNOMIAL
SEQUENCES
-
157
INTRODUCTION
-
157
DEFINITIONS
AND
FIRST
CHARACTERIZATIONS
-
158
SHEFFER
CLASSIFICATION
-
162
ALGEBRAIC
STRUCTURE
OF
THE
SET
G
-
164
MATRIX,
RECURRENCE
AND
DETERMINANT
FORMS
-
166
GENERATING
FUNCTION
-
168
GENERAL
PROPERTIES
-
170
RELATIONSHIP
WITH
MONOMIALITY
PRINCIPLE
-
171
DIFFERENTIAL
EQUATIONS
-
172
RELATIONSHIP
WITH
LINEAR
FUNCTIONAL
-
173
SOME
SPECIAL
SHEFFER
POLYNOMIAL
SEQUENCES
-
174
GENERALIZED
LAGUERRE
POLYNOMIALS
-
175
HERMITE
POLYNOMIALS
-
180
LOWER
FACTORIAL
AND
EXPONENTIAL
POLYNOMIALS
-
183
CENTRAL
FACTORIAL
AND
CARLITZ-RIORDAN
POLYNOMIALS
-
189
GENERALIZED
FALLING
FACTORIAL
AND
APPELL-BASED
FALLING
FACTORIAL
SEQUENCES
-
194
6.12
6.12.1
6.12.2
ORTHOGONAL
SHEFFER
POLYNOMIAL
SEQUENCES
-
200
INTRODUCTION
-
200
A
MATRIX
CALCULUS-BASED
APPROACH
TO
DETERMINE
THE
PREVIOUS
SHEFFER
RESULTS
-
202
6.12.3
ORTHOGONAL
A-TYPE
0
POLYNOMIALS
-
203
7
7.1
7.2
7.3
7.4
7.5
7.6
7.6.1
7.6.2
7.7
ORTHOGONAL
POLYNOMIAL
SEQUENCES
-
207
INTRODUCTION
-
207
DEFINITIONS
AND
SOME
PROPERTIES
-
209
MONIC
AND
ORTHONORMAL
POLYNOMIALS
-
217
THE
SYMMETRIC
CASE
-
219
ILLUSTRATIVE
EXAMPLES
-
220
ALGORITHMS
FOR
NUMERICALLY
GENERATING
ORTHOGONAL
POLYNOMIALS
-
227
CHEBYSHEV
ALGORITHM
-
227
NEW
ALGORITHMS
-
229
NUMERICAL
EXAMPLES
-
231
8
8.1
8.2
LIDSTONE
AND
CENTRAL
FACTORIAL-TYPE
POLYNOMIAL
SEQUENCES
-
238
INTRODUCTION
-
238
ODD
LIDSTONE-TYPE
POLYNOMIAL
SEQUENCES
-
239
XIV
-
-
CONTENTS
8.2.1
8.2.2
8.2.3
8.2.4
8.2.5
8.2.6
8.2.7
8.2.8
8.3
8.3.1
8.3.2
8.3.3
8.3.4
8.3.5
8.3.6
8.3.7
8.3.8
8.4
8.5
8.5.1
8.5.2
8.5.3
8.5.4
8.5.5
8.5.6
8.6
8.6.1
8.6.2
8.6.3
8.6.4
8.6.5
8.6.6
MATRIX
FORM
-
240
FIRST
RECURRENCE
RELATIONS
AND
RELATED
DETERMINANT
FORMS
-
242
SECOND
RECURRENCE
RELATION
AND
RELATED
DETERMINANT
FORM
-
243
DIFFERENTIAL
EQUATIONS
FOR
ODD
LIDSTONE-TYPE
POLYNOMIALS
-
246
OPERATIONAL
MATRICES
-
247
GENERATING
FUNCTION
-
250
RELATIONSHIP
WITH
APPELL
POLYNOMIAL
SEQUENCES
-
252
EXAMPLES
-
253
EVEN
LIDSTONE-TYPE
POLYNOMIAL
SEQUENCES
-
259
MATRIX
FORM
-
260
FIRST
RECURRENCE
RELATION
AND
RELATED
DETERMINANT
FORM
-
262
SECOND
RECURRENCE
RELATION
AND
RELATED
DETERMINANT
FORM
-
263
DIFFERENTIAL
EQUATIONS
FOR
EVEN
LIDSTONE-TYPE
POLYNOMIALS
-
264
OPERATIONAL
MATRICES
-
264
GENERATING
FUNCTION
-
265
RELATIONSHIP
WITH
APPELL
POLYNOMIAL
SEQUENCES
-
266
EXAMPLES
-
266
GENERAL
ODD
AND
EVEN
CENTRAL
FACTORIAL-TYPE
POLYNOMIAL
SEQUENCES
-
271
GENERAL
ODD
CENTRAL
FACTORIAL-TYPE
POLYNOMIAL
SEQUENCES
-
272
MATRIX
FORM
-
273
CONJUGATE
POLYNOMIAL
SEQUENCES
-
274
RECURRENCE
RELATIONS
AND
RELATED
DETERMINANT
FORMS
-
275
EXPONENTIAL
GENERATING
FUNCTION
-
277
CONNECTION
TO
THE
BASIS
MONOMIALS
X2/+1
-
278
EXAMPLES
-
280
GENERAL
EVEN
CENTRAL
FACTORIAL
POLYNOMIAL
SEQUENCES
-
283
MATRIX
FORM
-
284
CONJUGATE
EVEN
POLYNOMIALS
-
285
RECURRENCE
RELATION
AND
RELATED
DETERMINANT
FORM
-
286
GENERATING
FUNCTION
-
287
CONNECTION
TO
THE
BASIS
MONOMIALS
X2
-
288
EXAMPLES
-
289
9
9.1
9.2
9.3
9.4
9.5
BERNSTEIN
BASIS
-
293
INTRODUCTION
-
293
BERNSTEIN
BASIS
-
294
NUMERICAL
STABILITY
-
304
BASIS
TRANSFORMATIONS
-
306
GENERATING
FUNCTION
-
308
10
10.1
BIVARIATE
SPECIAL
POLYNOMIALS:
HINTS
-
310
INTRODUCTION
-
310
CONTENTS
-
XV
10.2
GENERAL
BIVARIATE
APPELL
POLYNOMIALS
-
311
10.2.1
DEFINITIONS
AND
FIRST
PROPERTIES
-
311
10.2.2
MATRIX
FORM
-
315
10.2.3
RECURRENCE
RELATIONS
-
318
10.2.4
DETERMINANT
FORMS
-
319
10.2.5
DIFFERENTIAL
OPERATORS
AND
EQUATIONS
-
322
10.2.6
RELATIONSHIP
WITH
MONOMIALITY
PRINCIPLES
-
322
10.2.7
GENERAL
PROPERTIES
-
323
10.2.8
RELATIONS
WITH
LINEAR
FUNCTIONAL
AND
LINEAR
INTERPOLATION
-
326
10.2.9
SOME
BIVARIATE
APPELL
SEQUENCES
-
327
10.3
GENERAL
BIVARIATE
LIDSTONE-TYPE
POLYNOMIALS
-
340
10.3.1
INTRODUCTION
-
340
10.3.2
GENERAL
BIVARIATE
ODD
LIDSTONE-TYPE
POLYNOMIAL
SEQUENCES
-
340
10.3.3
MATRIX
FORM
-
344
10.3.4
RECURRENCE
RELATIONS
AND
RELATED
DETERMINANT
FORMS
-
345
10.3.5
DIFFERENTIAL
EQUATION
-
346
10.3.6
GENERAL
PROPERTIES
-
346
10.3.7
SOME
BIVARIATE
ODD
LIDSTONE-TYPE
SEQUENCES
-
349
10.4
BIVARIATE
BERNSTEIN
BASIS
ON
THE
SIMPLEX
-
351
PART
III:
COMPUTATIONAL
APPLICATIONS
INTRODUCTION
-
359
11
APPROXIMATION
THEORY
BY
OPERATORS
-
361
11.1
BERNSTEIN
AND
BERNSTEIN-TYPE
OPERATORS
-
361
11.1.1
BERNSTEIN
'
S
THEOREM
-
362
11.1.2
ASYMPTOTIC
EXPANSION
-
366
11.1.3
SOME
ALGORITHMS
OF
POLYNOMIAL
EXTRAPOLATION
-
367
11.1.4
BUTZER
AND
MAY
POLYNOMIALS
-
369
11.1.5
TWO
INTERESTING
APPLICATIONS
-
370
11.1.6
NUMERICAL
EXAMPLES
-
371
11.1.7
RECENT
RESEARCH
-
373
11.1.8
BINOMIAL-TYPE
OR
BERNSTEIN-SHEFFER
OPERATORS
-
374
11.2
APPROXIMATION
OVER
A
SEMI-INFINITE
INTERVAL:
SZASZ
AND
SZASZ-TYPE
OPERATORS
-
376
11.2.1
ASYMPTOTIC
EXPANSION
AND
EXTRAPOLATION
FOR
OPERATORS
F
N
-
378
11.2.2
SPECIAL
CASES:
EXAMPLES
OF
OPERATORS.
OPERATORS
OF
JAKIMOVSKI
AND
LEVIATAN-TYPE
AND
ISMAIL-TYPE
-
379
11.2.3
NEW
OPERATORS
OF
JAKIMOVSKI
AND
LEVIATAN
TYPE
-
381
11.2.4
NEW
OPERATORS
OF
ISMAIL
TYPE
-
382
XVI
-
CONTENTS
11.2.5
11.3
COMPARISON
OF
RATE
OF
CONVERGENCE
-
384
NUMERICAL
EXAMPLES
-
385
12
12.1
12.2
12.3
12.4
12.4.1
12.4.2
12.4.3
12.4.4
12.4.5
12.5
12.6
12.7
INTERPOLATION
-
390
PRELIMINARIES
-
390
UMBRAL
BASIS
FOR
(L,
Q)
-
391
UMBRAL
INTERPOLATION
-
392
EXAMPLES
-
395
APPELL
INTERPOLATION
-
395
AH-APPELL
INTERPOLATION
-
398
VH,
6
H
-APPELL
INTERPOLATION
-
401
ABEL-SHEFFER
INTERPOLATION
[116]
-
401
^-SHEFFER
INTERPOLATION
-
403
SUMMARY
OF
UMBRAL
INTERPOLATION
FORMULAS
-
404
LIDSTONE-TYPE
POLYNOMIAL
INTERPOLATION:
PRELIMINARIES
-
404
THE
LIDSTONE-TYPE
AND
THE
GENERALIZED
LIDSTONE
INTERPOLATION
PROBLEM
-
410
12.8
12.9
12.9.1
12.9.2
12.10
12.11
12.12
EXPLICIT
ODD
AND
EVEN
LIDSTONE-TYPE
INTERPOLATING
POLYNOMIALS
-
412
EXAMPLES
-
415
LIDSTONE-BERNOULLI-TYPE
INTERPOLATING
POLYNOMIALS
-
416
LIDSTONE-EULER-TYPE
INTERPOLATING
POLYNOMIALS
-
421
SUMMARY
OF
LIDSTONE
INTERPOLATION
FORMULAS
-
425
NUMERICAL
EXAMPLES
-
425
ODD
AND
EVEN
CENTRAL
DIFFERENCE-TYPE
INTERPOLATION
-
429
13
13.1
13.2
13.3
13.3.1
BOUNDARY
VALUE
PROBLEMS
AND
POLYNOMIAL
SEQUENCES
-
430
INTRODUCTION
-
430
SPECTRAL
METHODS
-
431
A
SPECTRAL
METHOD
FOR
A
CLASS
OF
LINEAR
BOUNDARY
VALUE
PROBLEMS
-
431
BERNOULLI
POLYNOMIAL
SEQUENCES
FOR
THE
NUMERICAL
SOLUTION
OF
GENERAL
SECOND-ORDER
LINEAR
BVPS
-
431
13.3.2
13.3.3
13.3.4
13.4
THE
METHOD
-
433
NUMERICAL
COMPUTATION
OF
THE
SOLUTION
-
438
NUMERICAL
EXAMPLES
-
442
GENERAL
NONLINEAR
HIGH-ORDER
BVPS:
BIRKHOFF-LAGRANGE
COLLOCATION
METHODS
-
447
13.4.1
13.4.2
13.4.3
13.4.4
A
PRIORI
ESTIMATION
OF
ERROR
-
450
ALGORITHMS
AND
IMPLEMENTATION
-
451
SPECIAL
CASES
-
454
NUMERICAL
EXAMPLES
-
458
CONTENTS
-
XVII
14
14.1
14.2
14.2.1
14.2.2
14.3
14.3.1
APPELL
AND
LIDSTONE-TYPE
QUADRATURE
FORMULAS
-
463
INTRODUCTION
-
463
APPELL
QUADRATURE
RULES
-
463
APPELL
COMPOSITE
QUADRATURE
FORMULAS
-
466
EXAMPLES
-
469
LIDSTONE-TYPE
QUADRATURE
RULES
-
475
EXAMPLES
-
478
POSTFACE
-
485
BIBLIOGRAPHY
-
487
INDEX
-
503 |
| adam_txt |
CONTENTS
PREFACE
-
VII
PARTL:
BASIC
METHODS
INTRODUCTION
-
3
0
0.1
0.1.1
0.2
0.3
INFINITE
LOWER
TRIANGULAR
MATRICES
AND
FORMAL
POWER
SERIES
-
5
DEFINITIONS
AND
FIRST
PROPERTIES
-
5
HESSENBERG
DETERMINANTS
-
7
TRIANGULAR
TOEPLITZ
MATRICES
-
11
A
CLASS
OF
TRIDIAGONAL
MATRICES
AND
THE
RELATED
DETERMINANT
COMPUTATION
-
13
0.4
0.5
0.6
FORMAL
POWER
SERIES:
ALGEBRAIC
STRUCTURE
-
17
THE
^-SERIES
AND
COMPOSITIONAL
INVERSE
-
19
FORMAL
POWER
SERIES
WITH
ONLY
EVEN
POWERS
AND
RELATED
TOEPLITZ
MATRICES
-
25
0.7
0.8
0.9
0.9.1
0.9.2
0.9.3
0.10
0.11
APPELL-TYPE
MATRICES
-
26
SHEFFER-TYPE
MATRICES
-
34
LIDSTONE-TYPE
MATRICES
-
40
ODD
LIDSTONE-TYPE
MATRICES
-
40
EVEN
LIDSTONE-TYPE
MATRICES
-
44
RELATIONSHIP
BETWEEN
APPELL-TYPE
AND
LIDSTONE-TYPE
MATRICES
-
47
PRODUCTION
OR
STIELTJES
MATRIX
-
47
HANKEL
MATRICES
-
49
1
POLYNOMIAL
SEQUENCES:
ALGEBRAIC
STRUCTURE,
RECURRENCE
AND
DETERMINANT
FORM,
OPERATIONAL
METHODS
-
56
1.1
1.2
1.3
1.4
1.5
1.5.1
1.5.2
1.6
1.7
1.8
1.9
1.10
THE
LINEAR
SPACE
P
-
56
RECURRENCE
RELATIONS
-
59
DETERMINANT
FORMS
-
62
BASIS,
CONNECTION
CONSTANTS
AND
CONDITION
NUMBER
-
66
ILLUSTRATIVE
EXAMPLES
-
68
FIBONACCI
POLYNOMIAL
SEQUENCES
-
71
CHEBYSHEV
POLYNOMIAL
SEQUENCES
OF
THE
FIRST
KIND
-
78
COMPARISON
BETWEEN
CONDITION
NUMBERS
-
86
OPERATIONAL
MATRICES
-
88
DERIVATION
MATRIX:
CALCULATION
-
88
INTEGRATION
MATRIX:
CALCULATION
-
90
ILLUSTRATIVE
EXAMPLES
-
92
XII
-
CONTENTS
2
2.1
2.2
2.3
2.4
2.5
2.6
2.6.1
2.6.2
2.6.3
SYMMETRIC
POLYNOMIAL
SEQUENCES
-
97
DEFINITIONS
-
97
MATRIX
FORM
-
98
THE
ALGEBRAIC
STRUCTURE
-
99
RECURRENCE
RELATIONS
-
100
DETERMINANT
FORMS
-
102
ILLUSTRATIVE
EXAMPLES
-
105
ODD
AND
EVEN
FIBONACCI
POLYNOMIAL
SEQUENCES
-
105
ODD
AND
EVEN
CHEBYSHEV
POLYNOMIAL
SEQUENCES
OF
THE
FIRST
KIND
-
109
ODD
AND
EVEN
CENTRAL
FACTORIAL
POLYNOMIAL
SEQUENCES
-
113
3
3.1
3.2
3.3
3.4
GENERATING
FUNCTIONS
-
117
DEFINITIONS
-
117
SERIES
MANIPULATION
-
118
THE
FACTORIAL
FUNCTION
AND
THE
GENERALIZED
HYPERGEOMETRIC
FUNCTIONS
-
119
OBTAINING
GENERATING
FUNCTIONS
BY
REPRESENTATION
IN
MONOMIAL
POWER
-
121
4
4.1
4.2
DIFFERENTIAL
OPERATOR
AND
SHEFFER
CLASSIFICATION
-
129
THE
POLYNOMIAL
SET
ASSOCIATED
WITH
A
POLYNOMIAL
SEQUENCE
-
129
DIFFERENTIAL
OPERATOR
ASSOCIATED
WITH
POLYNOMIAL
SEQUENCE:
SHEFFER
'
S
CLASSIFICATION
-
131
4.3
4.3.1
4.3.2
4.3.3
4.3.4
4.4
4.4.1
4.4.2
4.4.3
ILLUSTRATIVE
EXAMPLES
-
133
MONIC
LAGUERRE
POLYNOMIALS
-
133
LAGUERRE
POLYNOMIALS
-
134
HERMITE
POLYNOMIALS
-
135
APPELL
POLYNOMIAL
SEQUENCES
-
135
APPELL-TYPE
1
POLYNOMIAL
SEQUENCES
-
136
MATRIX
FORM
-
138
RECURRENCE
RELATIONS
AND
DETERMINANT
FORMS
-
139
PARTICULAR
CASES
-
140
5
5.1
5.2
5.3
THE
MONOMIALITY
PRINCIPLE
-
143
INTRODUCTION
-
143
THE
DERIVATIVE
AND
MULTIPLICATIVE
OPERATORS
-
144
ILLUSTRATIVE
EXAMPLES
-
146
CONTENTS
-
XIII
PART
II:
SPECIAL
CLASSES
OF
POLYNOMIAL
SEQUENCES
INTRODUCTION
-
155
6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10
6.11
6.11.1
6.11.2
6.11.3
6.11.4
6.11.5
SHEFFER
POLYNOMIAL
SEQUENCES
-
157
INTRODUCTION
-
157
DEFINITIONS
AND
FIRST
CHARACTERIZATIONS
-
158
SHEFFER
CLASSIFICATION
-
162
ALGEBRAIC
STRUCTURE
OF
THE
SET
G
-
164
MATRIX,
RECURRENCE
AND
DETERMINANT
FORMS
-
166
GENERATING
FUNCTION
-
168
GENERAL
PROPERTIES
-
170
RELATIONSHIP
WITH
MONOMIALITY
PRINCIPLE
-
171
DIFFERENTIAL
EQUATIONS
-
172
RELATIONSHIP
WITH
LINEAR
FUNCTIONAL
-
173
SOME
SPECIAL
SHEFFER
POLYNOMIAL
SEQUENCES
-
174
GENERALIZED
LAGUERRE
POLYNOMIALS
-
175
HERMITE
POLYNOMIALS
-
180
LOWER
FACTORIAL
AND
EXPONENTIAL
POLYNOMIALS
-
183
CENTRAL
FACTORIAL
AND
CARLITZ-RIORDAN
POLYNOMIALS
-
189
GENERALIZED
FALLING
FACTORIAL
AND
APPELL-BASED
FALLING
FACTORIAL
SEQUENCES
-
194
6.12
6.12.1
6.12.2
ORTHOGONAL
SHEFFER
POLYNOMIAL
SEQUENCES
-
200
INTRODUCTION
-
200
A
MATRIX
CALCULUS-BASED
APPROACH
TO
DETERMINE
THE
PREVIOUS
SHEFFER
RESULTS
-
202
6.12.3
ORTHOGONAL
A-TYPE
0
POLYNOMIALS
-
203
7
7.1
7.2
7.3
7.4
7.5
7.6
7.6.1
7.6.2
7.7
ORTHOGONAL
POLYNOMIAL
SEQUENCES
-
207
INTRODUCTION
-
207
DEFINITIONS
AND
SOME
PROPERTIES
-
209
MONIC
AND
ORTHONORMAL
POLYNOMIALS
-
217
THE
SYMMETRIC
CASE
-
219
ILLUSTRATIVE
EXAMPLES
-
220
ALGORITHMS
FOR
NUMERICALLY
GENERATING
ORTHOGONAL
POLYNOMIALS
-
227
CHEBYSHEV
ALGORITHM
-
227
NEW
ALGORITHMS
-
229
NUMERICAL
EXAMPLES
-
231
8
8.1
8.2
LIDSTONE
AND
CENTRAL
FACTORIAL-TYPE
POLYNOMIAL
SEQUENCES
-
238
INTRODUCTION
-
238
ODD
LIDSTONE-TYPE
POLYNOMIAL
SEQUENCES
-
239
XIV
-
-
CONTENTS
8.2.1
8.2.2
8.2.3
8.2.4
8.2.5
8.2.6
8.2.7
8.2.8
8.3
8.3.1
8.3.2
8.3.3
8.3.4
8.3.5
8.3.6
8.3.7
8.3.8
8.4
8.5
8.5.1
8.5.2
8.5.3
8.5.4
8.5.5
8.5.6
8.6
8.6.1
8.6.2
8.6.3
8.6.4
8.6.5
8.6.6
MATRIX
FORM
-
240
FIRST
RECURRENCE
RELATIONS
AND
RELATED
DETERMINANT
FORMS
-
242
SECOND
RECURRENCE
RELATION
AND
RELATED
DETERMINANT
FORM
-
243
DIFFERENTIAL
EQUATIONS
FOR
ODD
LIDSTONE-TYPE
POLYNOMIALS
-
246
OPERATIONAL
MATRICES
-
247
GENERATING
FUNCTION
-
250
RELATIONSHIP
WITH
APPELL
POLYNOMIAL
SEQUENCES
-
252
EXAMPLES
-
253
EVEN
LIDSTONE-TYPE
POLYNOMIAL
SEQUENCES
-
259
MATRIX
FORM
-
260
FIRST
RECURRENCE
RELATION
AND
RELATED
DETERMINANT
FORM
-
262
SECOND
RECURRENCE
RELATION
AND
RELATED
DETERMINANT
FORM
-
263
DIFFERENTIAL
EQUATIONS
FOR
EVEN
LIDSTONE-TYPE
POLYNOMIALS
-
264
OPERATIONAL
MATRICES
-
264
GENERATING
FUNCTION
-
265
RELATIONSHIP
WITH
APPELL
POLYNOMIAL
SEQUENCES
-
266
EXAMPLES
-
266
GENERAL
ODD
AND
EVEN
CENTRAL
FACTORIAL-TYPE
POLYNOMIAL
SEQUENCES
-
271
GENERAL
ODD
CENTRAL
FACTORIAL-TYPE
POLYNOMIAL
SEQUENCES
-
272
MATRIX
FORM
-
273
CONJUGATE
POLYNOMIAL
SEQUENCES
-
274
RECURRENCE
RELATIONS
AND
RELATED
DETERMINANT
FORMS
-
275
EXPONENTIAL
GENERATING
FUNCTION
-
277
CONNECTION
TO
THE
BASIS
MONOMIALS
X2/+1
-
278
EXAMPLES
-
280
GENERAL
EVEN
CENTRAL
FACTORIAL
POLYNOMIAL
SEQUENCES
-
283
MATRIX
FORM
-
284
CONJUGATE
EVEN
POLYNOMIALS
-
285
RECURRENCE
RELATION
AND
RELATED
DETERMINANT
FORM
-
286
GENERATING
FUNCTION
-
287
CONNECTION
TO
THE
BASIS
MONOMIALS
X2
-
288
EXAMPLES
-
289
9
9.1
9.2
9.3
9.4
9.5
BERNSTEIN
BASIS
-
293
INTRODUCTION
-
293
BERNSTEIN
BASIS
-
294
NUMERICAL
STABILITY
-
304
BASIS
TRANSFORMATIONS
-
306
GENERATING
FUNCTION
-
308
10
10.1
BIVARIATE
SPECIAL
POLYNOMIALS:
HINTS
-
310
INTRODUCTION
-
310
CONTENTS
-
XV
10.2
GENERAL
BIVARIATE
APPELL
POLYNOMIALS
-
311
10.2.1
DEFINITIONS
AND
FIRST
PROPERTIES
-
311
10.2.2
MATRIX
FORM
-
315
10.2.3
RECURRENCE
RELATIONS
-
318
10.2.4
DETERMINANT
FORMS
-
319
10.2.5
DIFFERENTIAL
OPERATORS
AND
EQUATIONS
-
322
10.2.6
RELATIONSHIP
WITH
MONOMIALITY
PRINCIPLES
-
322
10.2.7
GENERAL
PROPERTIES
-
323
10.2.8
RELATIONS
WITH
LINEAR
FUNCTIONAL
AND
LINEAR
INTERPOLATION
-
326
10.2.9
SOME
BIVARIATE
APPELL
SEQUENCES
-
327
10.3
GENERAL
BIVARIATE
LIDSTONE-TYPE
POLYNOMIALS
-
340
10.3.1
INTRODUCTION
-
340
10.3.2
GENERAL
BIVARIATE
ODD
LIDSTONE-TYPE
POLYNOMIAL
SEQUENCES
-
340
10.3.3
MATRIX
FORM
-
344
10.3.4
RECURRENCE
RELATIONS
AND
RELATED
DETERMINANT
FORMS
-
345
10.3.5
DIFFERENTIAL
EQUATION
-
346
10.3.6
GENERAL
PROPERTIES
-
346
10.3.7
SOME
BIVARIATE
ODD
LIDSTONE-TYPE
SEQUENCES
-
349
10.4
BIVARIATE
BERNSTEIN
BASIS
ON
THE
SIMPLEX
-
351
PART
III:
COMPUTATIONAL
APPLICATIONS
INTRODUCTION
-
359
11
APPROXIMATION
THEORY
BY
OPERATORS
-
361
11.1
BERNSTEIN
AND
BERNSTEIN-TYPE
OPERATORS
-
361
11.1.1
BERNSTEIN
'
S
THEOREM
-
362
11.1.2
ASYMPTOTIC
EXPANSION
-
366
11.1.3
SOME
ALGORITHMS
OF
POLYNOMIAL
EXTRAPOLATION
-
367
11.1.4
BUTZER
AND
MAY
POLYNOMIALS
-
369
11.1.5
TWO
INTERESTING
APPLICATIONS
-
370
11.1.6
NUMERICAL
EXAMPLES
-
371
11.1.7
RECENT
RESEARCH
-
373
11.1.8
BINOMIAL-TYPE
OR
BERNSTEIN-SHEFFER
OPERATORS
-
374
11.2
APPROXIMATION
OVER
A
SEMI-INFINITE
INTERVAL:
SZASZ
AND
SZASZ-TYPE
OPERATORS
-
376
11.2.1
ASYMPTOTIC
EXPANSION
AND
EXTRAPOLATION
FOR
OPERATORS
F
N
-
378
11.2.2
SPECIAL
CASES:
EXAMPLES
OF
OPERATORS.
OPERATORS
OF
JAKIMOVSKI
AND
LEVIATAN-TYPE
AND
ISMAIL-TYPE
-
379
11.2.3
NEW
OPERATORS
OF
JAKIMOVSKI
AND
LEVIATAN
TYPE
-
381
11.2.4
NEW
OPERATORS
OF
ISMAIL
TYPE
-
382
XVI
-
CONTENTS
11.2.5
11.3
COMPARISON
OF
RATE
OF
CONVERGENCE
-
384
NUMERICAL
EXAMPLES
-
385
12
12.1
12.2
12.3
12.4
12.4.1
12.4.2
12.4.3
12.4.4
12.4.5
12.5
12.6
12.7
INTERPOLATION
-
390
PRELIMINARIES
-
390
UMBRAL
BASIS
FOR
(L,
Q)
-
391
UMBRAL
INTERPOLATION
-
392
EXAMPLES
-
395
APPELL
INTERPOLATION
-
395
AH-APPELL
INTERPOLATION
-
398
VH,
6
H
-APPELL
INTERPOLATION
-
401
ABEL-SHEFFER
INTERPOLATION
[116]
-
401
^-SHEFFER
INTERPOLATION
-
403
SUMMARY
OF
UMBRAL
INTERPOLATION
FORMULAS
-
404
LIDSTONE-TYPE
POLYNOMIAL
INTERPOLATION:
PRELIMINARIES
-
404
THE
LIDSTONE-TYPE
AND
THE
GENERALIZED
LIDSTONE
INTERPOLATION
PROBLEM
-
410
12.8
12.9
12.9.1
12.9.2
12.10
12.11
12.12
EXPLICIT
ODD
AND
EVEN
LIDSTONE-TYPE
INTERPOLATING
POLYNOMIALS
-
412
EXAMPLES
-
415
LIDSTONE-BERNOULLI-TYPE
INTERPOLATING
POLYNOMIALS
-
416
LIDSTONE-EULER-TYPE
INTERPOLATING
POLYNOMIALS
-
421
SUMMARY
OF
LIDSTONE
INTERPOLATION
FORMULAS
-
425
NUMERICAL
EXAMPLES
-
425
ODD
AND
EVEN
CENTRAL
DIFFERENCE-TYPE
INTERPOLATION
-
429
13
13.1
13.2
13.3
13.3.1
BOUNDARY
VALUE
PROBLEMS
AND
POLYNOMIAL
SEQUENCES
-
430
INTRODUCTION
-
430
SPECTRAL
METHODS
-
431
A
SPECTRAL
METHOD
FOR
A
CLASS
OF
LINEAR
BOUNDARY
VALUE
PROBLEMS
-
431
BERNOULLI
POLYNOMIAL
SEQUENCES
FOR
THE
NUMERICAL
SOLUTION
OF
GENERAL
SECOND-ORDER
LINEAR
BVPS
-
431
13.3.2
13.3.3
13.3.4
13.4
THE
METHOD
-
433
NUMERICAL
COMPUTATION
OF
THE
SOLUTION
-
438
NUMERICAL
EXAMPLES
-
442
GENERAL
NONLINEAR
HIGH-ORDER
BVPS:
BIRKHOFF-LAGRANGE
COLLOCATION
METHODS
-
447
13.4.1
13.4.2
13.4.3
13.4.4
A
PRIORI
ESTIMATION
OF
ERROR
-
450
ALGORITHMS
AND
IMPLEMENTATION
-
451
SPECIAL
CASES
-
454
NUMERICAL
EXAMPLES
-
458
CONTENTS
-
XVII
14
14.1
14.2
14.2.1
14.2.2
14.3
14.3.1
APPELL
AND
LIDSTONE-TYPE
QUADRATURE
FORMULAS
-
463
INTRODUCTION
-
463
APPELL
QUADRATURE
RULES
-
463
APPELL
COMPOSITE
QUADRATURE
FORMULAS
-
466
EXAMPLES
-
469
LIDSTONE-TYPE
QUADRATURE
RULES
-
475
EXAMPLES
-
478
POSTFACE
-
485
BIBLIOGRAPHY
-
487
INDEX
-
503 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Costabile, Francesco Gualtieri, Maria Italia 1962- Napoli, Anna 1969- |
| author_GND | (DE-588)173968651 (DE-588)1323198237 (DE-588)1321451636 |
| author_facet | Costabile, Francesco Gualtieri, Maria Italia 1962- Napoli, Anna 1969- |
| author_role | aut aut aut |
| author_sort | Costabile, Francesco |
| author_variant | f c fc m i g mi mig a n an |
| building | Verbundindex |
| bvnumber | BV049507024 |
| ctrlnum | (OCoLC)1417339894 (DE-599)DNB1299123546 |
| format | Book |
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| id | DE-604.BV049507024 |
| illustrated | Illustrated |
| index_date | 2024-07-03T23:22:30Z |
| indexdate | 2024-09-17T18:00:10Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110757231 3110757230 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034852059 |
| oclc_num | 1417339894 |
| open_access_boolean | |
| owner | DE-29T |
| owner_facet | DE-29T |
| physical | XVII, 506 Seiten Illustrationen 17 cm x 24 cm, 991 g |
| publishDate | 2024 |
| publishDateSearch | 2024 |
| publishDateSort | 2024 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter studies in mathematics |
| series2 | De Gruyter studies in mathematics |
| spelling | Costabile, Francesco Verfasser (DE-588)173968651 aut Polynomial sequences basic methods, special classes, and computational applications Francesco Aldo Costabile, Maria Italia Gualtieri, Anna Napoli Berlin ; Boston De Gruyter [2024] XVII, 506 Seiten Illustrationen 17 cm x 24 cm, 991 g txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematics Volume 96 Polynomsequenzen Numerische Analyse Infinitesimalrechnung echte Funktionen Polynomsequenzen; Numerische Analysis; Infinitesimalrechnung; Reelle Funktionen Polynomial sequences; Numerical Analysis; Infinitesimal calculus; Real-valued function Gualtieri, Maria Italia 1962- Verfasser (DE-588)1323198237 aut Napoli, Anna 1969- Verfasser (DE-588)1321451636 aut Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-075724-8 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-075732-3 De Gruyter studies in mathematics Volume 96 (DE-604)BV000005407 96 X:MVB https://www.degruyter.com/isbn/9783110757231 B:DE-101 application/pdf https://d-nb.info/1299123546/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034852059&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p vlb 20230812 DE-101 https://d-nb.info/provenance/plan#vlb |
| spellingShingle | Costabile, Francesco Gualtieri, Maria Italia 1962- Napoli, Anna 1969- Polynomial sequences basic methods, special classes, and computational applications De Gruyter studies in mathematics |
| title | Polynomial sequences basic methods, special classes, and computational applications |
| title_auth | Polynomial sequences basic methods, special classes, and computational applications |
| title_exact_search | Polynomial sequences basic methods, special classes, and computational applications |
| title_exact_search_txtP | Polynomial sequences basic methods, special classes, and computational applications |
| title_full | Polynomial sequences basic methods, special classes, and computational applications Francesco Aldo Costabile, Maria Italia Gualtieri, Anna Napoli |
| title_fullStr | Polynomial sequences basic methods, special classes, and computational applications Francesco Aldo Costabile, Maria Italia Gualtieri, Anna Napoli |
| title_full_unstemmed | Polynomial sequences basic methods, special classes, and computational applications Francesco Aldo Costabile, Maria Italia Gualtieri, Anna Napoli |
| title_short | Polynomial sequences |
| title_sort | polynomial sequences basic methods special classes and computational applications |
| title_sub | basic methods, special classes, and computational applications |
| url | https://www.degruyter.com/isbn/9783110757231 https://d-nb.info/1299123546/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034852059&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005407 |
| work_keys_str_mv | AT costabilefrancesco polynomialsequencesbasicmethodsspecialclassesandcomputationalapplications AT gualtierimariaitalia polynomialsequencesbasicmethodsspecialclassesandcomputationalapplications AT napolianna polynomialsequencesbasicmethodsspecialclassesandcomputationalapplications AT walterdegruytergmbhcokg polynomialsequencesbasicmethodsspecialclassesandcomputationalapplications |
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