Hypergeometric orthogonal polynomials and their q-analogues:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer-Verlag
[2010]
|
| Schriftenreihe: | Springer Monographs in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XIX, 578 Seiten |
| ISBN: | 9783642050138 |
Internformat
MARC
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| 100 | 1 | |a Koekoek, Roelof |4 aut | |
| 245 | 1 | 0 | |a Hypergeometric orthogonal polynomials and their q-analogues |c Roelof Koekoek ; Peter A. Lesky ; René F. Swarttouw ; Vorw. von Tom H. Koornwinder |
| 264 | 1 | |a Berlin ; Heidelberg |b Springer-Verlag |c [2010] | |
| 264 | 4 | |c © 2010 | |
| 300 | |a XIX, 578 Seiten | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Springer Monographs in Mathematics | |
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| 700 | 1 | |a Lesky, Peter |d 1926-2008 |0 (DE-588)137833105 |4 aut | |
| 700 | 1 | |a Swarttouw, René François |d 1964- |0 (DE-588)172944333 |4 aut | |
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Datensatz im Suchindex
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|---|---|
| adam_text |
CONTENTS FOREWORD V PREFACE XI 1 DEFINITIONS AND MISCELLANEOUS FORMULAS
1 1.1 ORTHOGONAL POLYNOMIALS 1 1.2 THE GAMMA AND BETA FUNCTION 3 1.3 THE
SHIFTED FACTORIAL AND BINOMIAL COEFFICIENTS 4 1.4 HYPERGEOMETRIC
FUNCTIONS 5 1.5 THE BINOMIAL THEOREM AND OTHER SUMMATION FORMULAS 7 1.6
SOME INTEGRALS 8 1.7 TRANSFORMATION FORMULAS 10 1.8 THE ^-SHIFTED
FACTORIAL 11 1.9 THE 7-GAMMA FUNCTION AND G-BINOMIAL COEFFICIENTS 13
1.10 BASIC HYPERGEOMETRIC FUNCTIONS 15 1.11 THE 7-BINOMIAL THEOREM AND
OTHER SUMMATION FORMULAS 16 1.12 MORE INTEGRALS 18 1.13 TRANSFORMATION
FORMULAS 19 1.14 SOME ^-ANALOGUES OF SPECIAL FUNCTIONS 22 1.15 THE Q-
DERIVATIVE AND /-INTEGRAL 24 1.16 SHIFT OPERATORS AND RODRIGUES-TYPE
FORMULAS 26 2 POLYNOMIAL SOLUTIONS OF EIGENVALUE PROBLEMS 29 2.1 HAHN'S
G-OPERATOR 29 2.2 EIGENVALUE PROBLEMS 30 2.3 THE REGULARITY CONDITION 33
2.4 DETERMINATION OF THE POLYNOMIAL SOLUTIONS 35 2.4.1 FIRST APPROACH 35
2.4.2 SECOND APPROACH 37 2.5 EXISTENCE OF A THREE-TERM RECURRENCE
RELATION 40 2.6 EXPLICIT FORM OF THE THREE-TERM RECURRENCE RELATION 45
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1000034070 DIGITALISIERT
DURCH XVI CONTENTS 3 ORTHOGONALITY OF THE POLYNOMIAL SOLUTIONS 53 3. 1
FAVARD'S THEOREM 53 3.2 ORTHOGONALITY AND THE SELF-ADJOINT OPERATOR
EQUATION 55 3.3 THE JACKSON-THOMAE ^-INTEGRAL 59 3.4 RODRIGUES FORMULAS
62 3.5 DUALITY 71 PART I CLASSICAL ORTHOGONAL POLYNOMIALS 4 ORTHOGONAL
POLYNOMIAL SOLUTIONS OF DIFFERENTIAL EQUATIONS 79 CONTINUOUS CLASSICAL
ORTHOGONAL POLYNOMIALS 79 4.1 POLYNOMIAL SOLUTIONS OF DIFFERENTIAL
EQUATIONS 79 4.2 CLASSIFICATION OF THE POSITIVE-DEFINITE ORTHOGONAL
POLYNOMIAL SOLUTIONS 80 4.3 PROPERTIES OF THE POSITIVE-DEFINITE
ORTHOGONAL POLYNOMIAL SOLUTIONS 83 5 ORTHOGONAL POLYNOMIAL SOLUTIONS OF
REAL DIFFERENCE EQUATIONS 95 DISCRETE CLASSICAL ORTHOGONAL POLYNOMIALS 1
95 5.1 POLYNOMIAL SOLUTIONS OF REAL DIFFERENCE EQUATIONS 95 5.2
CLASSIFICATION OF THE POSITIVE-DEFINITE ORTHOGONAL POLYNOMIAL SOLUTIONS
97 5.3 PROPERTIES OF THE POSITIVE-DEFINITE ORTHOGONAL POLYNOMIAL
SOLUTIONS 101 6 ORTHOGONAL POLYNOMIAL SOLUTIONS OF COMPLEX DIFFERENCE
EQUATIONS. 123 DISCRETE CLASSICAL ORTHOGONAL POLYNOMIALS II 123 6.1
REAL POLYNOMIAL SOLUTIONS OF COMPLEX DIFFERENCE EQUATIONS 123 6.2
CLASSIFICATION OF THE REAL POSITIVE-DEFINITE ORTHOGONAL POLYNOMIAL
SOLUTIONS 130 6.3 PROPERTIES OF THE POSITIVE-DEFINITE ORTHOGONAL
POLYNOMIAL SOLUTIONS 1 3 CONTENTS XVII 8 ORTHOGONAL POLYNOMIAL SOLUTIONS
IN Z(Z + ) OF COMPLEX DIFFERENCE EQUATIONS 171 DISCRETE CLASSICAL
ORTHOGONAL POLYNOMIALS IV 171 8.1 REAL POLYNOMIAL SOLUTIONS OF COMPLEX
DIFFERENCE EQUATIONS 171 8.2 ORTHOGONALITY RELATIONS FOR CONTINUOUS DUAL
HAHN POLYNOMIALS . 173 8.3 ORTHOGONALITY RELATIONS FOR WILSON
POLYNOMIALS 177 ASKEY SCHEME OF HYPERGEOMETRIC ORTHOGONAL POLYNOMIALS
183 9 HYPERGEOMETRIC ORTHOGONAL POLYNOMIALS 1 85 9.1 WILSON 185 9.2
RACAH 190 9.3 CONTINUOUS DUAL HAHN 196 9.4 CONTINUOUS HAHN 200 9.5 HAHN
204 9.6 DUAL HAHN 208 9.7 MEIXNER-POLLACZEK 213 9.8 JACOBI 216 9.8.1
GEGENBAUER / ULTRASPHERICAL 222 9.8.2 CHEBYSHEV 225 9.8.3 LEGENDRE /
SPHERICAL 229 9.9 PSEUDO JACOBI 231 9.10 MEIXNER 234 9.11 KRAWTCHOUK 237
9.12 LAGUERRE 241 9.13 BESSEL 244 9.14 CHARLIER 247 9.15 HERMITE 250
PART II CLASSICAL ^-ORTHOGONAL POLYNOMIALS 10 ORTHOGONAL POLYNOMIAL
SOLUTIONS OF ^-DIFFERENCE EQUATIONS 257 CLASSICAL G-ORTHOGONAL
POLYNOMIALS 1 257 10.1 POLYNOMIAL SOLUTIONS OF ^-DIFFERENCE EQUATIONS
257 10.2 THE BASIC HYPERGEOMETRIC REPRESENTATION 258 10. XVIII CONTENTS
11.4 ORTHOGONALITY AND THE SELF-ADJOINT OPERATOR EQUATION 329 11.5
RODRIGUES FORMULAS 333 11.6 CLASSIFICATION OF THE POSITIVE-DEFINITE
ORTHOGONAL POLYNOMIAL SOLUTIONS 334 11.7 SOLUTIONS OF THE G -1 -PEARSON
EQUATION 344 11.8 ORTHOGONALITY RELATIONS 354 12 ORTHOGONAL POLYNOMIAL
SOLUTIONS IN Q~~ X + UQ X OF REAL Y-DIFFERENCE EQUATIONS 369 CLASSICAL
G-ORTHOGONAL POLYNOMIALS III 369 12.1 MOTIVATION FOR POLYNOMIALS IN Q~ X
+ UQ X THROUGH DUALITY 369 12.2 DIFFERENCE EQUATIONS HAVING REAL
POLYNOMIAL SOLUTIONS WITH ARGUMENT Q~ X 4- UQ X 370 12.3 THE BASIC
HYPERGEOMETRIC REPRESENTATION 373 12.4 THE THREE-TERM RECURRENCE
RELATION 377 12.5 CLASSIFICATION OF THE POSITIVE-DEFINITE ORTHOGONAL
POLYNOMIAL SOLUTIONS 379 12.6 SOLUTIONS OF THE ^-PEARSON EQUATION 383
12.7 ORTHOGONALITY RELATIONS 389 13 ORTHOGONAL POLYNOMIAL SOLUTIONS IN F
+ ^ OF COMPLEX Q-DIFFERENCE EQUATIONS 395 CLASSICAL ^-ORTHOGONAL
POLYNOMIALS IV 395 13.1 REAL POLYNOMIAL SOLUTIONS IN | + F CONTENTS XIX
14.11 BIG 7-LAGUERRE 478 14.12 LITTLE 7-JACOBI 482 14.12.1 LITTLE
G-LEGENDRE 486 14.13 9-MEIXNER 488 14.14 QUANTUM G-KRAWTCHOUK 493 14.15
7-KRAWTCHOUK 496 14.16 AFFINE G-KRAWTCHOUK 501 14.17 DUAL G-KRAWTCHOUK
505 14.18 CONTINUOUS BIG G-HERMITE 509 14.19 CONTINUOUS G-LAGUERRE 514
14.20 LITTLE G-LAGUERRE/WALL 518 14.21 9-LAGUERRE 522 14.22 (7-BESSEL
526 14.23 9-CHARLIER 530 14.24 AL-SALAM-CARLITZ 1 534 14.25
AL-SALAM-CARLITZ II 537 14.26 CONTINUOUS G-HERMITE 540 14.27
STIELTJES-WIGERT 544 14.28 DISCRETE G-HERMITE I 547 14.29 DISCRETE
G-HERMITE II 550 BIBLIOGRAPHY 553 INDEX 575 |
| any_adam_object | 1 |
| author | Koekoek, Roelof Lesky, Peter 1926-2008 Swarttouw, René François 1964- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-sort | 3515.55 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-20T10:34:48Z |
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| isbn | 9783642050138 |
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| spelling | Koekoek, Roelof aut Hypergeometric orthogonal polynomials and their q-analogues Roelof Koekoek ; Peter A. Lesky ; René F. Swarttouw ; Vorw. von Tom H. Koornwinder Berlin ; Heidelberg Springer-Verlag [2010] © 2010 XIX, 578 Seiten txt rdacontent n rdamedia nc rdacarrier Springer Monographs in Mathematics Hypergeometrische orthogonale Polynome (DE-588)4161059-3 gnd rswk-swf Hypergeometrische orthogonale Polynome (DE-588)4161059-3 s DE-604 Lesky, Peter 1926-2008 (DE-588)137833105 aut Swarttouw, René François 1964- (DE-588)172944333 aut Erscheint auch als Online-Ausgabe 978-3-642-05014-5 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3423810&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020195296&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Koekoek, Roelof Lesky, Peter 1926-2008 Swarttouw, René François 1964- Hypergeometric orthogonal polynomials and their q-analogues Hypergeometrische orthogonale Polynome (DE-588)4161059-3 gnd |
| subject_GND | (DE-588)4161059-3 |
| title | Hypergeometric orthogonal polynomials and their q-analogues |
| title_auth | Hypergeometric orthogonal polynomials and their q-analogues |
| title_exact_search | Hypergeometric orthogonal polynomials and their q-analogues |
| title_full | Hypergeometric orthogonal polynomials and their q-analogues Roelof Koekoek ; Peter A. Lesky ; René F. Swarttouw ; Vorw. von Tom H. Koornwinder |
| title_fullStr | Hypergeometric orthogonal polynomials and their q-analogues Roelof Koekoek ; Peter A. Lesky ; René F. Swarttouw ; Vorw. von Tom H. Koornwinder |
| title_full_unstemmed | Hypergeometric orthogonal polynomials and their q-analogues Roelof Koekoek ; Peter A. Lesky ; René F. Swarttouw ; Vorw. von Tom H. Koornwinder |
| title_short | Hypergeometric orthogonal polynomials and their q-analogues |
| title_sort | hypergeometric orthogonal polynomials and their q analogues |
| topic | Hypergeometrische orthogonale Polynome (DE-588)4161059-3 gnd |
| topic_facet | Hypergeometrische orthogonale Polynome |
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