Orthogonal Polynomials
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Sections in KLS Chapter 1
- Orthogonal polynomials
- The gamma and beta function
- The shifted factorial and binomial coefficients
- Hypergeometric functions
- The binomial theorem and other summation formulas
- Some integrals
- Transformation formulas
- The q-shifted factorial
- The q-gamma function and q-binomial coefficients
- Basic hypergeometric functions
- The q-binomial theorem and other summation formulas
- More integrals
- Transformation formulas
- Some q-analogues of special functions
- The q-derivative and q-integral
- Shift operators and Rodrigues-type formulas
Sections in KLS Chapter 9
Sections in KLS Chapter 14
- Askey-Wilson
- q-Racah
- Continuous dual q-Hahn
- Continuous q-Hahn
- Big q-Jacobi
- Big q-Jacobi: Special case
- q-Hahn
- Dual q-Hahn
- Al-Salam-Chihara
- q-Meixner-Pollaczek
- Continuous q-Jacobi
- Continuous q-Jacobi: Special cases
- Big q-Laguerre
- Little q-Jacobi
- Little q-Jacobi: Special case
- q-Meixner
- Quantum q-Krawtchouk
- q-Krawtchouk
- Affine q-Krawtchouk
- Dual q-Krawtchouk
- Continuous big q-Hermite
- Continuous q-Laguerre
- Little q-Laguerre / Wall
- q-Laguerre
- q-Bessel
- q-Charlier
- Al-Salam-Carlitz I
- Al-Salam-Carlitz II
- Continuous q-Hermite
- Stieltjes-Wigert
- Discrete q-Hermite I
- Discrete q-Hermite II