Verfügbarkeit: Classical and quantum orthogonal polynomials in one variable

Classical and quantum orthogonal polynomials in one variable:

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Bibliographische Detailangaben
Format:	Buch
Sprache:	English
Veröffentlicht:	Cambridge [u.a.] Cambridge Univ. Press 2005
Ausgabe:	1. publ.
Schriftenreihe:	Encyclopedia of mathematics and its applications 98
Schlagworte:	Orthogonale Polynome Orthogonale reeksen Orthogonal polynomials
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XVIII, 706 S.
ISBN:	0521782015 9780521782012

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MARC


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245	1	0	\|a Classical and quantum orthogonal polynomials in one variable \|c Mourad E. H. Ismail. With two chapters by Walter van Assche
250			\|a 1. publ.
264		1	\|a Cambridge [u.a.] \|b Cambridge Univ. Press \|c 2005
300			\|a XVIII, 706 S.
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490	1		\|a Encyclopedia of mathematics and its applications \|v 98
650		7	\|a Orthogonale Polynome \|2 swd
650		7	\|a Orthogonale reeksen \|2 gtt
650		4	\|a Orthogonal polynomials
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700	1		\|a Van Assche, Walter \|d 1958- \|e Sonstige \|0 (DE-588)111317088 \|4 oth
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Datensatz im Suchindex

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adam_text	CLASSICAL AND QUANTUM ORTHOGONAL POLYNOMIALS IN ONE VARIABLE MOURAD E.H. ISMAIL UNIVERSITY OF CENTRAL FLORIDA WITH TWO CHAPTERS BY WALTER VAN ASSCHE CATHOLIC UNIVERSITY OFLEUVEN CAMBRIDGE UNIVERSITY PRESS CONTENTS FOREWORD . PAGE XI PREFACE XVI 1 PRELIMINARIES 1 1.1 HERMITIAN MATRICES AND QUADRATIC FORMS 1 1.2 SOME REAL AND COMPLEX ANALYSIS 3 1.3 SOME SPECIAL FUNCTIONS 8 1.4 SUMMATION THEOREMS AND TRANSFORMATIONS 12 2 ORTHOGONAL POLYNOMIALS 16 2.1 CONSTRUCTION OF ORTHOGONAL POLYNOMIALS 16 2.2 RECURRENCE RELATIONS 22 2.3 NUMERATOR POLYNOMIALS 26 2.4 QUADRATURE FORMULAS 28 2.5 THE SPECTRAL THEOREM 30 2.6 CONTINUED FRACTIONS 35 2.7 MODIFICATIONS OF MEASURES: CHRISTOFFEL AND UVAROV 37 2.8 MODIFICATIONS OF MEASURES: TODA 41 2.9 MODIFICATION BY ADDING FINITE DISCRETE PARTS 43 2.10 MODIFICATIONS OF RECURSION COEFFICIENTS . 45 2.11 DUAL SYSTEMS 47 3 DIFFERENTIAL EQUATIONS 52 3.1 PRELIMINARIES 52 3.2 DIFFERENTIAL EQUATIONS 53 3.3 APPLICATIONS 63 3.4 DISCRIMINANTS 67 3.5 AN ELECTROSTATIC EQUILIBRIUM PROBLEM 70 3.6 FUNCTIONS OF THE SECOND KIND 73 3.7 LIE ALGEBRAS 76 4 JACOBI POLYNOMIALS 80 4.1 ORTHOGONALITY 80 4.2 DIFFERENTIAL AND RECURSION FORMULAS 82 4.3 GENERATING FUNCTIONS 88 4.4 FUNCTIONS OF THE SECOND KIND 93 VI CONTENTS 4.5 ULTRASPHERICAL POLYNOMIALS 94 4.6 LAGUERRE AND HERMITE POLYNOMIALS 98 4.7 MULTILINEAR GENERATING FUNCTIONS 106 4.8 ASYMPTOTICS AND EXPANSIONS 115 4.9 RELATIVE EXTREMA OF CLASSICAL POLYNOMIALS *121 4.10 THE BESSEL POLYNOMIALS 123 5 SOME INVERSE PROBLEMS 133 5.1 ULTRASPHERICAL POLYNOMIALS 133 5.2 BIRTH AND DEATH PROCESSES 136 5.3 THE HADAMARD INTEGRAL 141 5.4 POLLACZEK POLYNOMIALS 147 5.5 A GENERALIZATION 151 5.6 ASSOCIATED LAGUERRE AND HERMITE POLYNOMIALS 158 5.7 ASSOCIATED JACOBI POLYNOMIALS 162 5.8 THE J-MATRIX METHOD 168 5.9 THE MEIXNER-POLLACZEK POLYNOMIALS 171 6 DISCRETE ORTHOGONAL POLYNOMIALS 174 6.1 MEIXNER POLYNOMIALS 174 6.2 HAHN, DUAL HAHN, AND KRAWTCHOUK POLYNOMIALS 177 6.3 DIFFERENCE EQUATIONS 186 6.4 DISCRETE DISCRIMINANTS 190 6.5 LOMMEL POLYNOMIALS 194 6.6 AN INVERSE OPERATOR 199 7 ZEROS AND INEQUALITIES 203 7.1 A THEOREM OF MARKOV --.. 203 7.2- _ CHAIN SEQUENCES 205 7.3 THE HELLMANN-FEYNMAN THEOREM 211 7.4 EXTREME ZEROS OF ORTHOGONAL POLYNOMIALS 219 7.5 CONCLUDING REMARKS 221 8 POLYNOMIALS ORTHOGONAL ON THE UNIT CIRCLE 222 8.1 ELEMENTARY PROPERTIES 222 8.2 RECURRENCE RELATIONS 225 8.3 DIFFERENTIAL EQUATIONS 231 8;4 FUNCTIONAL EQUATIONS AND ZEROS 240 8.5 LIMIT THEOREMS 244 8.6 MODIFICATIONS OF MEASURES 246 9 LINEARIZATION, CONNECTIONS AND INTEGRAL REPRESENTATIONS 253 9.1 CONNECTION COEFFICIENTS 255 9.2 THE ULTRASPHERICAL POLYNOMIALS AND WATSON S THEOREM 261 9.3 LINEARIZATION AND POWER SERIES COEFFICIENTS 263 9.4 LINEARIZATION OF PRODUCTS AND ENUMERATION 268 9.5 REPRESENTATIONS FOR JACOBI POLYNOMIALS 273 9.6 ADDITION AND PRODUCT FORMULAS 276 9.7 THE ASKEY-GASPER INEQUALITY 280 CONTENTS VII 10 11 12 13 14 15 THE 10.1 10.2 10.3 SHEFFER CLASSIFICATION PRELIMINARIES DELTA OPERATORS ALGEBRAIC THEORY (/-SERIES PRELIMINARIES 11.1 11.2 11.3 11.4 INTRODUCTION ORTHOGONAL POLYNOMIALS THE BOOTSTRAP METHOD (/-DIFFERENCES ^-SUMMATION THEOREMS 12.1 12.2 12.3 12.4 12.5 12.6 BASIC DEFINITIONS EXPANSION THEOREMS BILATERAL SERIES TRANSFORMATIONS ADDITIONAL TRANSFORMATIONS THETA FUNCTIONS SOME (/-ORTHOGONAL POLYNOMIALS 13.1 13.2 13.3 13.4 13.5 13.6 13.7 Q-HERMITE POLYNOMIALS (/-ULTRASPHERICAL POLYNOMIALS LINEARIZATION AND CONNECTION COEFFICIENTS ASYMPTOTICS APPLICATION: THE ROGERS-RAMANUJAN IDENTITIES RELATED ORTHOGONAL POLYNOMIALS THREE SYSTEMS OF (/-ORTHOGONAL POLYNOMIALS EXPONENTIAL AND G-BESSEL FUNCTIONS 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 THE 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 DEFINITIONS GENERATING FUNCTIONS ADDITION FORMULAS Q- ANALOGUES OF LOMMEL AND BESSEL POLYNOMIALS A CLASS OF ORTHOGONAL FUNCTIONS AN OPERATOR CALCULUS POLYNOMIALS OF (/-BINOMIAL TYPE ANOTHER G-UMBRAL CALCULUS - ASKEY-WILSON POLYNOMIALS THE AL-SALAM-CHIHARA POLYNOMIALS THE ASKEY-WILSON POLYNOMIALS REMARKS ASYMPTOTICS CONTINUOUS (/-JACOBI POLYNOMIALS AND DISCRIMINANTS Q-RACAH POLYNOMIAL S (/-INTEGRAL REPRESENTATIONS LINEAR AND MULTILINEAR GENERATING FUNCTIONS ASSOCIATED (/-ULTRASPHERICAL POLYNOMIALS 15.10 TWO SVSTEMS OF ORTHOEONAL POLVNOMIALS 282 282 285 287 293 293 293 294 296 299 299 302 307 310 313 315 318 319 326 330 334 335 340 344 351 351 356 358 359 . 363 365 371 375 377 377 381 386 388 390 395 399 404 410 415 VIII CONTENTS 16 THE ASKEY-WILSON OPERATORS 425 16.1 BASIC RESULTS 425 16.2 A G-STURM-LIOUVILLE OPERATOR 432 16.3 THE ASKEY-WILSON POLYNOMIALS 436 16.4 CONNECTION COEFFICIENTS 442 16.5 BETHE ANSATZ EQUATIONS OF XXZ MODEL 445 17 (/-HERMITE POLYNOMIALS ON THE UNIT CIRCLE , 454 17.1 THE ROGERS-SZEGO POLYNOMIALS 454 17.2 GENERALIZATIONS 459 17.3 (/-DIFFERENCE EQUATIONS 463 18 DISCRETE (/-ORTHOGONAL POLYNOMIALS 468 18.1 DISCRETE STURM-LIOUVILLE PROBLEMS 468 18.2 THE AL-SALAM-CARLITZ POLYNOMIALS 469 18.3 THE AL-SALAM-CARLITZ MOMENT PROBLEM 475 18.4 Q-JACOBI POLYNOMIALS 476 18.5 G-HAHN POLYNOMIALS 483 18.6 (/-DIFFERENCES AND QUANTIZED DISCRIMINANTS 485 18.7 A FAMILY OF BIORTHOGONAL RATIONAL FUNCTIONS 487 19 FRACTIONAL AND (/-FRACTIONAL CALCULUS 490 19.1 THE RIEMANN-LIOUVILLE OPERATORS 490 19.2 BILINEAR FORMULAS 494 19.3 EXAMPLES 495 19.4 G-FRACTIONAL CALCULUS 500 19.5 SOME INTEGRAL OPERATORS 503 20 POLYNOMIAL SOLUTIONS TO FUNCTIONAL EQUATIONS 508 20. 1- BOCHNER S THEOREM 508 20.2 DIFFERENCE AND (/-DIFFERENCE EQUATIONS 513 20.3 EQUATIONS IN THE ASKEY-WILSON OPERATORS , 515 20.4 LEONARD PAIRS AND THE (/-RACAH POLYNOMIALS 517 20.5 CHARACTERIZATION THEOREMS 524 21 SOME INDETERMINATE MOMENT PROBLEMS 529 21.1 THEHAMBURGER MOMENT PROBLEM 529 21.2 A SYSTEM OF ORTHOGONAL POLYNOMIALS , 533 21.3 GENERATING FUNCTIONS 536 21.4 THE NEVANLINNA MATRIX 541 21.5 SOME ORTHOGONALITY MEASURES 543 21.6 LADDER OPERATORS 546 21.7 ZEROS 549 21.8 THE Q-LAGUERRE MOMENT PROBLEM 552 21.9 OTHER INDETERMINATE MOMENT PROBLEMS 562 21.10 SOME BIORTHOGONAL RATIONAL FUNCTIONS 571 22 THE RIEMANN-HILBERT PROBLEM 577 22.1 THE CAUCHY TRANSFORM 577 CONTENTS IX 22.2 THE FOKAS-ITS-KITAEV BOUNDARY VALUE PROBLEM 580 22.2.1 THE THREE-TERM RECURRENCE RELATION 583 22.3 HERMITE POLYNOMIALS 585 22.3.1 A DIFFERENTIAL EQUATION 585 22.4 LAGUERRE POLYNOMIALS 588 22.4.1 THREE-TERM RECURRENCE RELATION 590 22.4.2 A DIFFERENTIAL EQUATION 591 22.5 JACOBI POLYNOMIALS 595 22.5.1 DIFFERENTIAL EQUATION 596 22.6 ASYMPTOTIC BEHAVIOR 600 22.7 DISCRETE ORTHOGONAL POLYNOMIALS 602 22.8 EXPONENTIAL WEIGHTS 603 23 MULTIPLE ORTHOGONAL POLYNOMIALS 606 23.1 TYPE I AND II MULTIPLE ORTHOGONAL POLYNOMIALS 607 23.1.1 ANGELESCO SYSTEMS 609 23.1.2 AT SYSTEMS 610 23.1.3 BIORTHOGONALITY 612 23.1.4 RECURRENCE RELATIONS 613 23.2 HERMITE-PADE APPROXIMATION 620 23.3 MULTIPLE JACOBI POLYNOMIALS 621 23.3.1 JACOBI-ANGELESCO POLYNOMIALS 621 23.3.2 JACOBI-PINEIRO POLYNOMIALS 625 23.4 MULTIPLE LAGUERRE POLYNOMIALS 627 23.4.1 MULTIPLE LAGUERRE POLYNOMIALS OF THE FIRST KIND 627 23.4.2 MULTIPLE LAGUERRE POLYNOMIALS OF THE SECOND KIND 628 23.5 MULTIPLE HERMITE POLYNOMIALS 629 23.5.1 RANDOM MATRICES WITH EXTERNAL SOURCE 630 23.6 DISCRETE MULTIPLE ORTHOGONAL POLYNOMIALS 631 23.6.1 MULTIPLE CHARLIER POLYNOMIALS 631 23.6.2 MULTIPLE MEIXNER POLYNOMIALS N 631 23.6.3 MULTIPLE KRAWTCHOUK POLYNOMIALS 633 23.6.4 MULTIPLE HAHN POLYNOMIALS 633 23.6.5 MULTIPLE LITTLE Q- JACOBI POLYNOMIALS 634 23.7 MODIFIED BESSEL FUNCTION WEIGHTS . 635 23.7.1 MODIFIED BESSEL FUNCTIONS 636 23.8 RIEMANN-HILBERT PROBLEM 638 23.8.1 RECURRENCE RELATION 643 23.8.2 DIFFERENTIAL EQUATION FOR MULTIPLE HERMITE POLYNOMIALS 644 24 RESEARCH PROBLEMS 647 24.1 MULTIPLE ORTHOGONAL POLYNOMIALS 647 24.2 A CLASS OF ORTHOGONAL FUNCTIONS 648 24.3 POSITIVITY 648 24.4 ASYMPTOTICS AND MOMENT PROBLEMS 649 24.5 FUNCTIONAL EQUATIONS AND LIE ALGEBRAS 651 X CONTENTS 24.6 ROGERS-RAMANUJAN IDENTITIES 652 24.7 CHARACTERIZATION THEOREMS 653 24.8 SPECIAL SYSTEMS OF ORTHOGONAL POLYNOMIALS 657 24.9 ZEROS OF ORTHOGONAL POLYNOMIALS 660 BIBLIOGRAPHY 661 INDEX 697 AUTHOR INDEX 703
adam_txt	CLASSICAL AND QUANTUM ORTHOGONAL POLYNOMIALS IN ONE VARIABLE MOURAD E.H. ISMAIL UNIVERSITY OF CENTRAL FLORIDA WITH TWO CHAPTERS BY WALTER VAN ASSCHE CATHOLIC UNIVERSITY OFLEUVEN CAMBRIDGE UNIVERSITY PRESS CONTENTS FOREWORD . PAGE XI PREFACE XVI 1 PRELIMINARIES 1 1.1 HERMITIAN MATRICES AND QUADRATIC FORMS 1 1.2 SOME REAL AND COMPLEX ANALYSIS 3 1.3 SOME SPECIAL FUNCTIONS 8 1.4 SUMMATION THEOREMS AND TRANSFORMATIONS 12 2 ORTHOGONAL POLYNOMIALS 16 2.1 CONSTRUCTION OF ORTHOGONAL POLYNOMIALS 16 2.2 RECURRENCE RELATIONS 22 2.3 NUMERATOR POLYNOMIALS 26 2.4 QUADRATURE FORMULAS 28 2.5 THE SPECTRAL THEOREM 30 2.6 CONTINUED FRACTIONS 35 2.7 MODIFICATIONS OF MEASURES: CHRISTOFFEL AND UVAROV 37 2.8 MODIFICATIONS OF MEASURES: TODA \ 41 2.9 MODIFICATION BY ADDING FINITE DISCRETE PARTS \ 43 2.10 MODIFICATIONS OF RECURSION COEFFICIENTS . 45 2.11 DUAL SYSTEMS 47 3 DIFFERENTIAL EQUATIONS 52 3.1 PRELIMINARIES 52 3.2 DIFFERENTIAL EQUATIONS 53 3.3 APPLICATIONS 63 3.4 DISCRIMINANTS 67 3.5 AN ELECTROSTATIC EQUILIBRIUM PROBLEM 70 3.6 FUNCTIONS OF THE SECOND KIND 73 3.7 LIE ALGEBRAS 76 4 JACOBI POLYNOMIALS 80 4.1 ORTHOGONALITY 80 4.2 DIFFERENTIAL AND RECURSION FORMULAS 82 4.3 GENERATING FUNCTIONS 88 4.4 FUNCTIONS OF THE SECOND KIND 93 VI CONTENTS 4.5 ULTRASPHERICAL POLYNOMIALS 94 4.6 LAGUERRE AND HERMITE POLYNOMIALS 98 4.7 MULTILINEAR GENERATING FUNCTIONS 106 4.8 ASYMPTOTICS AND EXPANSIONS 115 4.9 RELATIVE EXTREMA OF CLASSICAL POLYNOMIALS *121 4.10 THE BESSEL POLYNOMIALS 123 5 SOME INVERSE PROBLEMS 133 5.1 ULTRASPHERICAL POLYNOMIALS 133 5.2 BIRTH AND DEATH PROCESSES 136 5.3 THE HADAMARD INTEGRAL 141 5.4 POLLACZEK POLYNOMIALS 147 5.5 A GENERALIZATION 151 5.6 ASSOCIATED LAGUERRE AND HERMITE POLYNOMIALS 158 5.7 ASSOCIATED JACOBI POLYNOMIALS 162 5.8 THE J-MATRIX METHOD 168 5.9 THE MEIXNER-POLLACZEK POLYNOMIALS 171 6 DISCRETE ORTHOGONAL POLYNOMIALS 174 6.1 MEIXNER POLYNOMIALS 174 6.2 HAHN, DUAL HAHN, AND KRAWTCHOUK POLYNOMIALS 177 6.3 DIFFERENCE EQUATIONS 186 6.4 DISCRETE DISCRIMINANTS 190 6.5 LOMMEL POLYNOMIALS 194 6.6 AN INVERSE OPERATOR 199 7 ZEROS AND INEQUALITIES 203 7.1 A THEOREM OF MARKOV --. 203 7.2- _ CHAIN SEQUENCES 205 7.3 THE HELLMANN-FEYNMAN THEOREM 211 7.4 EXTREME ZEROS OF ORTHOGONAL POLYNOMIALS 219 7.5 CONCLUDING REMARKS 221 8 POLYNOMIALS ORTHOGONAL ON THE UNIT CIRCLE 222 8.1 ELEMENTARY PROPERTIES 222 8.2 RECURRENCE RELATIONS 225 8.3 DIFFERENTIAL EQUATIONS 231 8;4 FUNCTIONAL EQUATIONS AND ZEROS 240 8.5 LIMIT THEOREMS 244 8.6 MODIFICATIONS OF MEASURES 246 9 LINEARIZATION, CONNECTIONS AND INTEGRAL REPRESENTATIONS 253 9.1 CONNECTION COEFFICIENTS 255 9.2 THE ULTRASPHERICAL POLYNOMIALS AND WATSON'S THEOREM 261 9.3 LINEARIZATION AND POWER SERIES COEFFICIENTS 263 9.4 LINEARIZATION OF PRODUCTS AND ENUMERATION 268 9.5 REPRESENTATIONS FOR JACOBI POLYNOMIALS 273 9.6 ADDITION AND PRODUCT FORMULAS 276 9.7 THE ASKEY-GASPER INEQUALITY 280 CONTENTS VII 10 11 12 13 14 15 THE 10.1 10.2 10.3 SHEFFER CLASSIFICATION PRELIMINARIES DELTA OPERATORS ALGEBRAIC THEORY (/-SERIES PRELIMINARIES 11.1 11.2 11.3 11.4 INTRODUCTION ORTHOGONAL POLYNOMIALS THE BOOTSTRAP METHOD (/-DIFFERENCES ^-SUMMATION THEOREMS 12.1 12.2 12.3 12.4 12.5 12.6 BASIC DEFINITIONS EXPANSION THEOREMS BILATERAL SERIES TRANSFORMATIONS ADDITIONAL TRANSFORMATIONS THETA FUNCTIONS SOME (/-ORTHOGONAL POLYNOMIALS 13.1 13.2 13.3 13.4 13.5 13.6 13.7 Q-HERMITE POLYNOMIALS (/-ULTRASPHERICAL POLYNOMIALS LINEARIZATION AND CONNECTION COEFFICIENTS ASYMPTOTICS APPLICATION: THE ROGERS-RAMANUJAN IDENTITIES RELATED ORTHOGONAL POLYNOMIALS THREE SYSTEMS OF (/-ORTHOGONAL POLYNOMIALS EXPONENTIAL AND G-BESSEL FUNCTIONS 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 THE 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 DEFINITIONS GENERATING FUNCTIONS ADDITION FORMULAS Q- ANALOGUES OF LOMMEL AND BESSEL POLYNOMIALS A CLASS OF ORTHOGONAL FUNCTIONS AN OPERATOR CALCULUS POLYNOMIALS OF (/-BINOMIAL TYPE ANOTHER G-UMBRAL CALCULUS - ASKEY-WILSON POLYNOMIALS THE AL-SALAM-CHIHARA POLYNOMIALS THE ASKEY-WILSON POLYNOMIALS REMARKS ASYMPTOTICS CONTINUOUS (/-JACOBI POLYNOMIALS AND DISCRIMINANTS Q-RACAH POLYNOMIAL S (/-INTEGRAL REPRESENTATIONS LINEAR AND MULTILINEAR GENERATING FUNCTIONS ASSOCIATED (/-ULTRASPHERICAL POLYNOMIALS 15.10 TWO SVSTEMS OF ORTHOEONAL POLVNOMIALS 282 282 285 287 293 293 293 294 296 299 299 302 307 310 313 315 318 319 326 330 334 335 340 344 351 351 356 358 \ 359 . 363 365 371 375 " 377 377 381 386 388 390 395 399 404 410 415 VIII CONTENTS 16 THE ASKEY-WILSON OPERATORS 425 16.1 BASIC RESULTS 425 16.2 A G-STURM-LIOUVILLE OPERATOR 432 16.3 THE ASKEY-WILSON POLYNOMIALS 436 16.4 CONNECTION COEFFICIENTS 442 16.5 BETHE ANSATZ EQUATIONS OF XXZ MODEL 445 17 (/-HERMITE POLYNOMIALS ON THE UNIT CIRCLE , 454 17.1 THE ROGERS-SZEGO POLYNOMIALS 454 17.2 GENERALIZATIONS 459 17.3 (/-DIFFERENCE EQUATIONS 463 18 DISCRETE (/-ORTHOGONAL POLYNOMIALS 468 18.1 DISCRETE STURM-LIOUVILLE PROBLEMS 468 18.2 THE AL-SALAM-CARLITZ POLYNOMIALS 469 18.3 THE AL-SALAM-CARLITZ MOMENT PROBLEM 475 18.4 Q-JACOBI POLYNOMIALS 476 18.5 G-HAHN POLYNOMIALS 483 18.6 (/-DIFFERENCES AND QUANTIZED DISCRIMINANTS 485 18.7 A FAMILY OF BIORTHOGONAL RATIONAL FUNCTIONS 487 19 FRACTIONAL AND (/-FRACTIONAL CALCULUS 490 19.1 THE RIEMANN-LIOUVILLE OPERATORS 490 19.2 BILINEAR FORMULAS 494 19.3 EXAMPLES 495 19.4 G-FRACTIONAL CALCULUS 500 19.5 SOME INTEGRAL OPERATORS 503 20 POLYNOMIAL SOLUTIONS TO FUNCTIONAL EQUATIONS' 508 20. 1- BOCHNER'S THEOREM 508 20.2 DIFFERENCE AND (/-DIFFERENCE EQUATIONS 513 20.3 EQUATIONS IN THE ASKEY-WILSON OPERATORS , 515 20.4 LEONARD PAIRS AND THE (/-RACAH POLYNOMIALS 517 20.5 CHARACTERIZATION THEOREMS 524 21 SOME INDETERMINATE MOMENT PROBLEMS 529 21.1 THEHAMBURGER MOMENT PROBLEM 529 21.2 A SYSTEM OF ORTHOGONAL POLYNOMIALS , 533 21.3 GENERATING FUNCTIONS 536 21.4 THE NEVANLINNA MATRIX 541 21.5 SOME ORTHOGONALITY MEASURES 543 21.6 LADDER OPERATORS 546 21.7 ZEROS ' 549 21.8 THE Q-LAGUERRE MOMENT PROBLEM 552 21.9 OTHER INDETERMINATE MOMENT PROBLEMS 562 21.10 SOME BIORTHOGONAL RATIONAL FUNCTIONS 571 22 THE RIEMANN-HILBERT PROBLEM 577 22.1 THE CAUCHY TRANSFORM 577 CONTENTS IX 22.2 THE FOKAS-ITS-KITAEV BOUNDARY VALUE PROBLEM 580 22.2.1 THE THREE-TERM RECURRENCE RELATION 583 22.3 HERMITE POLYNOMIALS 585 22.3.1 A DIFFERENTIAL EQUATION 585 22.4 LAGUERRE POLYNOMIALS 588 22.4.1 THREE-TERM RECURRENCE RELATION 590 22.4.2 A DIFFERENTIAL EQUATION 591 22.5 JACOBI POLYNOMIALS 595 22.5.1 DIFFERENTIAL EQUATION 596 22.6 ASYMPTOTIC BEHAVIOR 600 22.7 DISCRETE ORTHOGONAL POLYNOMIALS 602 22.8 EXPONENTIAL WEIGHTS 603 23 MULTIPLE ORTHOGONAL POLYNOMIALS 606 23.1 TYPE I AND II MULTIPLE ORTHOGONAL POLYNOMIALS 607 23.1.1 ANGELESCO SYSTEMS 609 23.1.2 AT SYSTEMS 610 23.1.3 BIORTHOGONALITY 612 23.1.4 RECURRENCE RELATIONS 613 23.2 HERMITE-PADE APPROXIMATION 620 23.3 MULTIPLE JACOBI POLYNOMIALS 621 23.3.1 JACOBI-ANGELESCO POLYNOMIALS 621 23.3.2 JACOBI-PINEIRO POLYNOMIALS 625 23.4 MULTIPLE LAGUERRE POLYNOMIALS 627 23.4.1 MULTIPLE LAGUERRE POLYNOMIALS OF THE FIRST KIND 627 23.4.2 MULTIPLE LAGUERRE POLYNOMIALS OF THE SECOND KIND 628 23.5 MULTIPLE HERMITE POLYNOMIALS 629 23.5.1 RANDOM MATRICES WITH EXTERNAL SOURCE 630 23.6 DISCRETE MULTIPLE ORTHOGONAL POLYNOMIALS 631 23.6.1 MULTIPLE CHARLIER POLYNOMIALS \ 631 23.6.2 MULTIPLE MEIXNER POLYNOMIALS N 631 23.6.3 MULTIPLE KRAWTCHOUK POLYNOMIALS 633 23.6.4 MULTIPLE HAHN POLYNOMIALS 633 23.6.5 MULTIPLE LITTLE Q- JACOBI POLYNOMIALS 634 23.7 MODIFIED BESSEL FUNCTION WEIGHTS . 635 23.7.1 MODIFIED BESSEL FUNCTIONS 636 23.8 RIEMANN-HILBERT PROBLEM 638 23.8.1 RECURRENCE RELATION 643 23.8.2 DIFFERENTIAL EQUATION FOR MULTIPLE HERMITE POLYNOMIALS 644 24 RESEARCH PROBLEMS 647 24.1 MULTIPLE ORTHOGONAL POLYNOMIALS 647 24.2 A CLASS OF ORTHOGONAL FUNCTIONS 648 24.3 POSITIVITY 648 24.4 ASYMPTOTICS AND MOMENT PROBLEMS 649 24.5 FUNCTIONAL EQUATIONS AND LIE ALGEBRAS 651 X CONTENTS 24.6 ROGERS-RAMANUJAN IDENTITIES 652 24.7 CHARACTERIZATION THEOREMS 653 24.8 SPECIAL SYSTEMS OF ORTHOGONAL POLYNOMIALS 657 24.9 ZEROS OF ORTHOGONAL POLYNOMIALS 660 BIBLIOGRAPHY 661 INDEX 697 AUTHOR INDEX 703
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indexdate	2024-07-09T20:28:28Z
institution	BVB
isbn	0521782015 9780521782012
language	English
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physical	XVIII, 706 S.
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series	Encyclopedia of mathematics and its applications
series2	Encyclopedia of mathematics and its applications
spelling	Classical and quantum orthogonal polynomials in one variable Mourad E. H. Ismail. With two chapters by Walter van Assche 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2005 XVIII, 706 S. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 98 Orthogonale Polynome swd Orthogonale reeksen gtt Orthogonal polynomials Orthogonale Polynome (DE-588)4172863-4 gnd rswk-swf Orthogonale Polynome (DE-588)4172863-4 s DE-604 Ismail, Mourad E. H. Sonstige oth Van Assche, Walter 1958- Sonstige (DE-588)111317088 oth Encyclopedia of mathematics and its applications 98 (DE-604)BV000903719 98 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014278861&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Classical and quantum orthogonal polynomials in one variable Encyclopedia of mathematics and its applications Orthogonale Polynome swd Orthogonale reeksen gtt Orthogonal polynomials Orthogonale Polynome (DE-588)4172863-4 gnd
subject_GND	(DE-588)4172863-4
title	Classical and quantum orthogonal polynomials in one variable
title_auth	Classical and quantum orthogonal polynomials in one variable
title_exact_search	Classical and quantum orthogonal polynomials in one variable
title_exact_search_txtP	Classical and quantum orthogonal polynomials in one variable
title_full	Classical and quantum orthogonal polynomials in one variable Mourad E. H. Ismail. With two chapters by Walter van Assche
title_fullStr	Classical and quantum orthogonal polynomials in one variable Mourad E. H. Ismail. With two chapters by Walter van Assche
title_full_unstemmed	Classical and quantum orthogonal polynomials in one variable Mourad E. H. Ismail. With two chapters by Walter van Assche
title_short	Classical and quantum orthogonal polynomials in one variable
title_sort	classical and quantum orthogonal polynomials in one variable
topic	Orthogonale Polynome swd Orthogonale reeksen gtt Orthogonal polynomials Orthogonale Polynome (DE-588)4172863-4 gnd
topic_facet	Orthogonale Polynome Orthogonale reeksen Orthogonal polynomials
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014278861&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000903719
work_keys_str_mv	AT ismailmouradeh classicalandquantumorthogonalpolynomialsinonevariable AT vanasschewalter classicalandquantumorthogonalpolynomialsinonevariable

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