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q-Laguerre polynomials

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11: 18.1 Notation
Classical OP’s
Hahn Class OP’s
Wilson Class OP’s
Nor do we consider the shifted Jacobi polynomials: …or the dilated Chebyshev polynomials of the first and second kinds: …
12: 29.19 Physical Applications
§29.19 Physical Applications
§29.19(ii) Lamé Polynomials
13: 18.21 Hahn Class: Interrelations
§18.21 Hahn Class: Interrelations
§18.21(i) Dualities
§18.21(ii) Limit Relations and Special Cases
Hahn Jacobi
Meixner Laguerre
14: 18.9 Recurrence Relations and Derivatives
§18.9(iii) Derivatives
Jacobi
Ultraspherical
Laguerre
Hermite
15: 18.14 Inequalities
Legendre
Jacobi
Laguerre
Hermite
Jacobi
16: 18.8 Differential Equations
Table 18.8.1: Classical OP’s: differential equations A ( x ) f ′′ ( x ) + B ( x ) f ( x ) + C ( x ) f ( x ) + λ n f ( x ) = 0 .
# f ( x ) A ( x ) B ( x ) C ( x ) λ n
4 C n ( λ ) ( x ) 1 x 2 ( 2 λ + 1 ) x 0 n ( n + 2 λ )
8 L n ( α ) ( x ) x α + 1 x 0 n
12 H n ( x ) 1 2 x 0 2 n
14 𝐻𝑒 n ( x ) 1 x 0 n
17: 18.36 Miscellaneous Polynomials
§18.36 Miscellaneous Polynomials
§18.36(i) Jacobi-Type Polynomials
§18.36(ii) Sobolev Orthogonal Polynomials
§18.36(iv) Orthogonal Matrix Polynomials
§18.36(vi) Exceptional Orthogonal Polynomials
18: 18.37 Classical OP’s in Two or More Variables
§18.37(i) Disk Polynomials
Definition in Terms of Jacobi Polynomials
Definition in Terms of Jacobi Polynomials
Orthogonal polynomials associated with root systems are certain systems of trigonometric polynomials in several variables, symmetric under a certain finite group (Weyl group), and orthogonal on a torus. …For general q they occur as Macdonald polynomials for root system A n , as Macdonald polynomials for general root systems, and as Macdonald–Koornwinder polynomials; see Macdonald (1995, Chapter VI), Macdonald (2000, 2003), Koornwinder (1992).
19: 24.4 Basic Properties
§24.4(i) Difference Equations
§24.4(ii) Symmetry
Next, …
§24.4(vi) Special Values
§24.4(vii) Derivatives
20: 18.10 Integral Representations
Ultraspherical
Legendre
Jacobi
Ultraspherical
Laguerre