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Hahn class orthogonal polynomials

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1: 18.24 Hahn Class: Asymptotic Approximations
§18.24 Hahn Class: Asymptotic Approximations
Similar approximations are included for Jacobi, Krawtchouk, and Meixner polynomials.
2: 18.19 Hahn Class: Definitions
§18.19 Hahn Class: Definitions
Hahn, Krawtchouk, Meixner, and Charlier
Table 18.19.1: Orthogonality properties for Hahn, Krawtchouk, Meixner, and Charlier OP’s: discrete sets, weight functions, normalizations, and parameter constraints.
p n ( x ) X w x h n
Table 18.19.2: Hahn, Krawtchouk, Meixner, and Charlier OP’s: leading coefficients.
p n ( x ) k n
k n = ( 2 sin ϕ ) n n ! .
3: 18.20 Hahn Class: Explicit Representations
§18.20(i) Rodrigues Formulas
§18.20(ii) Hypergeometric Function and Generalized Hypergeometric Functions
4: 18.1 Notation
( z 1 , , z k ; q ) = ( z 1 ; q ) ( z k ; q ) .
Hahn Class OP’s
5: 18.21 Hahn Class: Interrelations
§18.21 Hahn Class: Interrelations
§18.21(i) Dualities
§18.21(ii) Limit Relations and Special Cases
See accompanying text
Figure 18.21.1: Askey scheme. … Magnify
6: 18.27 q -Hahn Class
§18.27 q -Hahn Class
§18.27(ii) q -Hahn Polynomials
§18.27(iii) Big q -Jacobi Polynomials
§18.27(iv) Little q -Jacobi Polynomials
§18.27(v) q -Laguerre Polynomials
7: 18.29 Asymptotic Approximations for q -Hahn and Askey–Wilson Classes
§18.29 Asymptotic Approximations for q -Hahn and Askey–Wilson Classes
8: 18.23 Hahn Class: Generating Functions
§18.23 Hahn Class: Generating Functions
Hahn
9: 18.22 Hahn Class: Recurrence Relations and Differences
§18.22(i) Recurrence Relations in n
§18.22(ii) Difference Equations in x
§18.22(iii) x -Differences
10: 13.6 Relations to Other Functions
Charlier Polynomials