Classical orthogonal polynomials of a discrete variable:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Berlin [u.a.]
Springer
1991
|
| Series: | Springer series in computational physics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | XVI, 374 S. graph. Darst. |
| ISBN: | 3540511237 0387511237 |
Staff View
MARC
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| 100 | 1 | |a Nikiforov, Arnol'd F. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Klassičeskie ortogonal'nye polinomy diskretnoj peremenoj |
| 245 | 1 | 0 | |a Classical orthogonal polynomials of a discrete variable |c A. F. Nikiforov ; S. K. Suslov ; V. B. Uvarov |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1991 | |
| 300 | |a XVI, 374 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer series in computational physics | |
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 7 | |a Analyse multidimensionnelle |2 ram | |
| 650 | 7 | |a Fonctions spéciales |2 ram | |
| 650 | 7 | |a Physique mathématique |2 ram | |
| 650 | 7 | |a Polynômes orthogonaux |2 ram | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Functions, Special | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Multivariate analysis | |
| 650 | 4 | |a Orthogonal polynomials | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
1. Classical Orthogonal Polynomials 2
1.1 An Equation of Hypergeometric Type 2
1.2 Polynomials of Hypergeometric Type and Their Derivatives.
The Rodrigues Formula 3
1.3 The Orthogonality Property 6
1.4 The Jacobi, Laguerre, and Hermite Polynomials 8
1.4.1 Classification of Polynomials 9
1.4.2 General Properties of Orthogonal Polynomials ...... 11
1.5 Classical Orthogonal Polynomials as Eigenfunctions
of Some Eigenvalue Problems 15
2. Classical Orthogonal Polynomials
of a Discrete Variable 18
2.1 The Difference Equation of Hypergeometric Type 18
2.2 Finite Difference Analogs of Polynomials
of Hypergeometric Type and of Their Derivatives.
The Rodrigues Type Formula 23
2.3 The Orthogonality Property 26
2.4 The Hahn, Chebyshev, Meixner, Kravchuk,
and Charlier Polynomials 30
2.5 Calculation of Main Characteristics 40
2.6 Asymptotic Properties. Connection with the Jacobi,
Laguerre, and Hermite Polynomials 45
2.7 Representation in Terms
of Generalized Hypergeometric Functions 49
3. Classical Orthogonal Polynomials
of a Discrete Variable on Nonuniform Lattices 55
3.1 The Difference Equation of Hypergeometric Type
on a Nonuniform Lattice 55
3.2 The Difference Analogs of Hypergeometric Type
Polynomials. The Rodrigues Formula. 62
3.3 The Orthogonality Property 70
3.4 Classification of Lattices 73
3.5 Classification of Polynomial Systems on Linear
and Quadratic Lattices.
The Racah and the Dual Hahn Polynomials 74
XIII
3.6 ^ Analogs of Polynomials Orthogonal on Linear
and Quadratic Lattices 78
3.6.1 The q Analogs of the Hahn, Meixner, Kravchuk,
and Charlier Polynomials on the Lattices
x(s) = exp(2ws) and x(s) = sinh(2ws) 79
3.6.2 The g Analogs of the Racah
and Dual Hahn Polynomials on the Lattices
x(s) = cosh(2a;s) and x(s) = cos(2u s) 90
3.6.3 Tables of Basic Data for g Analogs 99
3.7 Calculation of the Leading Coefficients
and Squared Norms. Tables of Data 99
3.8 Asymptotic Properties of the Racah
and Dual Hahn Polynomials 109
3.9 Construction of Some Orthogonal Polynomials
on Nonuniform Lattices by Means
of the Darboux Christoffel Formula Ill
3.10 Continuous Orthogonality 115
3.11 Representation in Terms of Hypergeometric
and g Hypergeometric Functions 132
3.12 Particular Solutions of the Hypergeometric Type
Difference Equation 155
Addendum to Chapter 3 167
4. Classical Orthogonal Polynomials
of a Discrete Variable in Applied Mathematics 170
4.1 Quadrature Formulas of Gaussian Type 170
4.2 Compression of Information by Means
of the Hahn Polynomials 175
4.3 Spherical Harmonics Orthogonal on a Discrete Set
of Points 179
4.4 Some Finite Difference Methods of Solution
of Partial Differential Equations 190
4.5 Systems of Differential Equations
with Constant Coefficients. The Genetic Model of Moran
and Some Problems of the Queueing Theory 194
4.6 Elementary Applications to Probability Theory 206
4.7 Estimation of the Packaging Capacity
of Metric Spaces 212
5. Classical Orthogonal Polynomials of a Discrete Variable
and the Representations of the Rotation Group 221
5.1 Generalized Spherical Functions and Their Relations
with Jacobi and Kravchuk Polynomials 222
5.1.1 The Three Dimensional Rotation Group
and Its Irreducible Representations 222
XIV
5.1.2 Expressing the Generalized Spherical Functions
in Terms of the Jacobi and Kravchuk Polynomials .. 232
5.1.3 Major Properties
of Generalized Spherical Functions 236
5.2 Clebsch Gordan Coefficients and Hahn Polynomials 240
5.2.1 The Tensor Product
of the Rotation Group Representations 240
5.2.2 Expressing the Clebsch Gordan Coefficients in Terms
of Hahn Polynomials 243
5.2.3 Main Properties of the Clebsch Gordan Coefficients . 248
5.2.4 Irreducible Tensor Operators.
The Wigner Eckart Theorem 253
5.3 The Wigner 6j Symbols and the Racah Polynomials 255
5.3.1 The Racah Coefficients and the Wigner 6j Symbols . 255
5.3.2 Expressing the 6,; Symbols Through
the Racah Polynomials 257
5.3.3 Main Properties of the 6j Symbols 260
5.4 The Wigner 9j Symbols as Orthogonal Polynomials
in Two Discrete Variables 264
5.4.1 The 9j Symbpls and the Relation
with the Clebsch Gordan Coefficients 264
5.4.2 The Polynomial Expression for the 9j Symbols 266
5.4.3 Basic Properties of the Polynomials Related
to the 9j Symbols 267
5.5 The Classical Orthogonal Polynomials
of a Discrete Variable in Some Problems
of Group Representation Theory 270
5.5.1 The Hahn Polynomials and the Representations
of the Rotation Group in the Four Dimensional Space 271
5.5.2 The Unitary Irreducible Representations
of the Lorentz Group SO(1,3)
and Hahn Polynomials in an Imaginary Argument ... 274
5.5.3 The Racah Polynomials and the Representations
of the Group SU(3) 278
5.5.4 The Charlier Polynomials and Representations
of the Heisenberg Weyl Group 281
6. Hyperspherical Harmonics 284
6.1 Spherical Coordinates in a Euclidean Space 284
6.1.1 Setting up Spherical Coordinates 285
6.1.2 A Metric and Elementary Volume 286
6.1.3 The Laplace Operator 288
6.1.4 A Graphical Approach 289
6.2 Solution of the n Dimensional Laplace Equation
in Spherical Coordinates 297
XV
6.2.1 Separation of Variables 297
6.2.2 Hyperspherical Harmonics 299
6.2.3 Illustrative Examples 302
6.3 Transformation of Harmonics Derived
in Different Spherical Coordinates 306
6.3.1 Transpositions and Transplants 306
6.3.2 The T Coefficients
for a Transplant Involving Closed Nodes 309
6.3.3 Open Nodes 313
6.4 Solution of the Schrodinger Equation
for the n Dimensional Harmonic Oscillator 320
6.4.1 Wave Functions of the Harmonic Oscillator
in n Dimensions 320
6.4.2 Transformation Between Wave Functions
of the Oscillator in Cartesian
and Spherical Coordinates 322
6.4.3 The T Coefficients as the 3nj Symbols of SU(1,1) .. 329
6.4.4 Matrix Elements of SU(1,1) 335
6.4.5 Harmonic Oscillator and Matrix Elements
of the Heisenberg Weyl Group N(3) 338
Addendum to Chapter 6 342
Bibliography 345
Subject Index 373
XVI
|
| any_adam_object | 1 |
| author | Nikiforov, Arnol'd F. Suslov, Sergej K. Uvarov, Vasilij B. 1929-1997 |
| author_GND | (DE-588)11086932X |
| author_facet | Nikiforov, Arnol'd F. Suslov, Sergej K. Uvarov, Vasilij B. 1929-1997 |
| author_role | aut aut aut |
| author_sort | Nikiforov, Arnol'd F. |
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| building | Verbundindex |
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| callnumber-first | Q - Science |
| callnumber-label | QC20 |
| callnumber-raw | QC20.7.O75 |
| callnumber-search | QC20.7.O75 |
| callnumber-sort | QC 220.7 O75 |
| callnumber-subject | QC - Physics |
| classification_rvk | SK 470 SK 540 SK 680 |
| classification_tum | MAT 338f MAT 266f MAT 052f |
| ctrlnum | (OCoLC)21482058 (DE-599)BVBBV006089698 |
| dewey-full | 515/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.55 |
| dewey-search | 515/.55 |
| dewey-sort | 3515 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre | Differenzgleichung gnd |
| genre_facet | Differenzgleichung |
| id | DE-604.BV006089698 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:40:07Z |
| institution | BVB |
| isbn | 3540511237 0387511237 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003845612 |
| oclc_num | 21482058 |
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| physical | XVI, 374 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in computational physics |
| spelling | Nikiforov, Arnol'd F. Verfasser aut Klassičeskie ortogonal'nye polinomy diskretnoj peremenoj Classical orthogonal polynomials of a discrete variable A. F. Nikiforov ; S. K. Suslov ; V. B. Uvarov Berlin [u.a.] Springer 1991 XVI, 374 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in computational physics Aus dem Russ. übers. Analyse multidimensionnelle ram Fonctions spéciales ram Physique mathématique ram Polynômes orthogonaux ram Mathematische Physik Functions, Special Mathematical physics Multivariate analysis Orthogonal polynomials Hypergeometrische Differenzengleichung (DE-588)4285388-6 gnd rswk-swf Klassische orthogonale Polynome (DE-588)4285387-4 gnd rswk-swf Diskrete Variable (DE-588)4365922-6 gnd rswk-swf Orthogonale Polynome (DE-588)4172863-4 gnd rswk-swf Differenzgleichung gnd rswk-swf Orthogonale Polynome (DE-588)4172863-4 s DE-604 Diskrete Variable (DE-588)4365922-6 s Differenzgleichung f Hypergeometrische Differenzengleichung (DE-588)4285388-6 s Klassische orthogonale Polynome (DE-588)4285387-4 s Suslov, Sergej K. Verfasser aut Uvarov, Vasilij B. 1929-1997 Verfasser (DE-588)11086932X aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003845612&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nikiforov, Arnol'd F. Suslov, Sergej K. Uvarov, Vasilij B. 1929-1997 Classical orthogonal polynomials of a discrete variable Analyse multidimensionnelle ram Fonctions spéciales ram Physique mathématique ram Polynômes orthogonaux ram Mathematische Physik Functions, Special Mathematical physics Multivariate analysis Orthogonal polynomials Hypergeometrische Differenzengleichung (DE-588)4285388-6 gnd Klassische orthogonale Polynome (DE-588)4285387-4 gnd Diskrete Variable (DE-588)4365922-6 gnd Orthogonale Polynome (DE-588)4172863-4 gnd |
| subject_GND | (DE-588)4285388-6 (DE-588)4285387-4 (DE-588)4365922-6 (DE-588)4172863-4 |
| title | Classical orthogonal polynomials of a discrete variable |
| title_alt | Klassičeskie ortogonal'nye polinomy diskretnoj peremenoj |
| title_auth | Classical orthogonal polynomials of a discrete variable |
| title_exact_search | Classical orthogonal polynomials of a discrete variable |
| title_full | Classical orthogonal polynomials of a discrete variable A. F. Nikiforov ; S. K. Suslov ; V. B. Uvarov |
| title_fullStr | Classical orthogonal polynomials of a discrete variable A. F. Nikiforov ; S. K. Suslov ; V. B. Uvarov |
| title_full_unstemmed | Classical orthogonal polynomials of a discrete variable A. F. Nikiforov ; S. K. Suslov ; V. B. Uvarov |
| title_short | Classical orthogonal polynomials of a discrete variable |
| title_sort | classical orthogonal polynomials of a discrete variable |
| topic | Analyse multidimensionnelle ram Fonctions spéciales ram Physique mathématique ram Polynômes orthogonaux ram Mathematische Physik Functions, Special Mathematical physics Multivariate analysis Orthogonal polynomials Hypergeometrische Differenzengleichung (DE-588)4285388-6 gnd Klassische orthogonale Polynome (DE-588)4285387-4 gnd Diskrete Variable (DE-588)4365922-6 gnd Orthogonale Polynome (DE-588)4172863-4 gnd |
| topic_facet | Analyse multidimensionnelle Fonctions spéciales Physique mathématique Polynômes orthogonaux Mathematische Physik Functions, Special Mathematical physics Multivariate analysis Orthogonal polynomials Hypergeometrische Differenzengleichung Klassische orthogonale Polynome Diskrete Variable Orthogonale Polynome Differenzgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003845612&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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