Contents
- Preface
- Definitions and miscellaneous formulas
- 0.1
- Introduction
- 0.2
- The q-shifted factorials
- 0.3
- The q-gamma function and the q-binomial coefficient
- 0.4
- Hypergeometric and basic hypergeometric functions
- 0.5
- The q-binomial theorem and other summation formulas
- 0.6
- Transformation formulas
- 0.7
- Some special functions and their q-analogues
- 0.8
- The q-derivative and the q-integral
- 0.9
- Shift operators and Rodrigues-type formulas
- ASKEY-SCHEME
- 1
- Hypergeometric orthogonal polynomials
- 1.1
- Wilson
- 1.2
- Racah
- 1.3
- Continuous dual Hahn
- 1.4
- Continuous Hahn
- 1.5
- Hahn
- 1.6
- Dual Hahn
- 1.7
- Meixner-Pollaczek
- 1.8
- Jacobi
- 1.8.1
- Gegenbauer / Ultraspherical
- 1.8.2
- Chebyshev
- 1.8.3
- Legendre / Spherical
- 1.9
- Meixner
- 1.10
- Krawtchouk
- 1.11
- Laguerre
- 1.12
- Charlier
- 1.13
- Hermite
- 2
- Limit relations between hypergeometric orthogonal polynomials
- 2.1
- Wilson
- 2.2
- Racah
- 2.3
- Continuous dual Hahn
- 2.4
- Continuous Hahn
- 2.5
- Hahn
- 2.6
- Dual Hahn
- 2.7
- Meixner-Pollaczek
- 2.8
- Jacobi
- 2.8.1
- Gegenbauer / Ultraspherical
- 2.9
- Meixner
- 2.10
- Krawtchouk
- 2.11
- Laguerre
- 2.12
- Charlier
- 2.13
- Hermite
- q-SCHEME
- 3
- Basic hypergeometric orthogonal polynomials
- 3.1
- Askey-Wilson
- 3.2
- q-Racah
- 3.3
- Continuous dual q-Hahn
- 3.4
- Continuous q-Hahn
- 3.5
- Big q-Jacobi
- 3.5.1
- Big q-Legendre
- 3.6
- q-Hahn
- 3.7
- Dual q-Hahn
- 3.8
- Al-Salam-Chihara
- 3.9
- q-Meixner-Pollaczek
- 3.10
- Continuous q-Jacobi
- 3.10.1
- Continuous q-ultraspherical / Rogers
- 3.10.2
- Continuous q-Legendre
- 3.11
- Big q-Laguerre
- 3.12
- Little q-Jacobi
- 3.12.1
- Little q-Legendre
- 3.13
- q-Meixner
- 3.14
- Quantum q-Krawtchouk
- 3.15
- q-Krawtchouk
- 3.16
- Affine q-Krawtchouk
- 3.17
- Dual q-Krawtchouk
- 3.18
- Continuous big q-Hermite
- 3.19
- Continuous q-Laguerre
- 3.20
- Little q-Laguerre / Wall
- 3.21
- q-Laguerre
- 3.22
- Alternative q-Charlier
- 3.23
- q-Charlier
- 3.24
- Al-Salam-Carlitz I
- 3.25
- Al-Salam-Carlitz II
- 3.26
- Continuous q-Hermite
- 3.27
- Stieltjes-Wigert
- 3.28
- Discrete q-Hermite I
- 3.29
- Discrete q-Hermite II
- 4
- Limit relations between basic hypergeometric orthogonal polynomials
- 4.1
- Askey-Wilson
- 4.2
- q-Racah
- 4.3
- Continuous dual q-Hahn
- 4.4
- Continuous q-Hahn
- 4.5
- Big q-Jacobi
- 4.6
- q-Hahn
- 4.7
- Dual q-Hahn
- 4.8
- Al-Salam-Chihara
- 4.9
- q-Meixner-Pollaczek
- 4.10
- Continuous q-Jacobi
- 4.10.1
- Continuous q-ultraspherical / Rogers
- 4.11
- Big q-Laguerre
- 4.12
- Little q-Jacobi
- 4.13
- q-Meixner
- 4.14
- Quantum q-Krawtchouk
- 4.15
- q-Krawtchouk
- 4.16
- Affine q-Krawtchouk
- 4.17
- Dual q-Krawtchouk
- 4.18
- Continuous big q-Hermite
- 4.19
- Continuous q-Laguerre
- 4.20
- Little q-Laguerre / Wall
- 4.21
- q-Laguerre
- 4.22
- Alternative q-Charlier
- 4.23
- q-Charlier
- 4.24
- Al-Salam-Carlitz I
- 4.25
- Al-Salam-Carlitz II
- 4.26
- Continuous q-Hermite
- 4.27
- Stieltjes-Wigert
- 4.28
- Discrete q-Hermite I
- 4.29
- Discrete q-Hermite II
- 5
- From basic to classical hypergeometric orthogonal polynomials
- 5.1
- Askey-Wilson --> Wilson
- 5.2
- q-Racah --> Racah
- 5.3
- Continuous dual q-Hahn --> Continuous dual Hahn
- 5.4
- Continuous q-Hahn --> Continuous Hahn
- 5.5
- Big q-Jacobi --> Jacobi
- 5.5.1
- Big q-Legendre --> Legendre / Spherical
- 5.6
- q-Hahn --> Hahn
- 5.7
- Dual q-Hahn --> Dual Hahn
- 5.8
- Al-Salam-Chihara --> Meixner-Pollaczek
- 5.9
- q-Meixner-Pollaczek --> Meixner-Pollaczek
- 5.10
- Continuous q-Jacobi --> Jacobi
- 5.10.1
- Continuous q-ultraspherical / Rogers --> Gegenbauer / Ultraspherical
- 5.10.2
- Continuous q-Legendre --> Legendre / Spherical
- 5.11
- Big q-Laguerre --> Laguerre
- 5.12
- Little q-Jacobi --> Jacobi / Laguerre
- 5.12.1
- Little q-Legendre --> Legendre / Spherical
- 5.13
- q-Meixner --> Meixner
- 5.14
- Quantum q-Krawtchouk --> Krawtchouk
- 5.15
- q-Krawtchouk --> Krawtchouk
- 5.16
- Affine q-Krawtchouk --> Krawtchouk
- 5.17
- Dual q-Krawtchouk --> Krawtchouk
- 5.18
- Continuous big q-Hermite --> Hermite
- 5.19
- Continuous q-Laguerre --> Laguerre
- 5.20
- Little q-Laguerre / Wall --> Laguerre / Charlier
- 5.21
- q-Laguerre --> Laguerre / Charlier
- 5.22
- Alternative q-Charlier --> Charlier
- 5.23
- q-Charlier --> Charlier
- 5.24
- Al-Salam-Carlitz I --> Charlier / Hermite
- 5.25
- Al-Salam-Carlitz II --> Charlier / Hermite
- 5.26
- Continuous q-Hermite --> Hermite
- 5.27
- Stieltjes-Wigert --> Hermite
- 5.28
- Discrete q-Hermite I --> Hermite
- 5.29
- Discrete q-Hermite II --> Hermite
- Bibliography
- Index
Last modified on March 30, 2001