Nevai–Blumenthal class

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11: 18.29 Asymptotic Approximations for $q$ -Hahn and Askey–Wilson Classes

§18.29 Asymptotic Approximations for $q$ -Hahn and Askey–Wilson Classes

…

12: 18.25 Wilson Class: Definitions

§18.25 Wilson Class: Definitions

… ►For the Wilson class OP’s

p_{n}(x)

with

x=\lambda(y)

: if the

y

-orthogonality set is

\{0,1,\dots,N\}

, then the role of the differentiation operator

\ifrac{\mathrm{d}}{\mathrm{d}x}

in the Jacobi, Laguerre, and Hermite cases is played by the operator

\Delta_{y}

followed by division by

\Delta_{y}(\lambda(y))

, or by the operator

\nabla_{y}

followed by division by

\nabla_{y}(\lambda(y))

. …The Wilson class consists of two discrete families (Racah and dual Hahn) and two continuous families (Wilson and continuous dual Hahn). … ►

§18.25(ii) Weights and Standardizations: Continuous Cases

… ►

Table 18.25.2: Wilson class OP’s: leading coefficients.

► ►►

$p_{n}(x)$	$k_{n}$
…

►

13: 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

14: 18.1 Notation

… ►

\left(z_{1},\dots,z_{k};q\right)_{\infty}=\left(z_{1};q\right)_{\infty}\cdots% \left(z_{k};q\right)_{\infty}.

… ►

Hahn Class OP’s

… ►

Wilson Class OP’s

… ►

$q$ -Hahn Class OP’s

… ►

Askey–Wilson Class OP’s

…

15: 16.27 Software

… ►For another listing of Web-accessible software for the functions in this chapter, see GAMS (class C19). …

16: 23.24 Software

… ►For another listing of Web-accessible software for the functions in this chapter, see GAMS (class C15). …

17: 18.20 Hahn Class: Explicit Representations

§18.20 Hahn Class: Explicit Representations

►

§18.20(i) Rodrigues Formulas

… ►

§18.20(ii) Hypergeometric Function and Generalized Hypergeometric Functions

…

18: 18.26 Wilson Class: Continued

§18.26 Wilson Class: Continued

… ►

§18.26(ii) Limit Relations

… ►

§18.26(iii) Difference Relations

… ►

§18.26(iv) Generating Functions

… ►

§18.26(v) Asymptotic Approximations

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19: 18.27 $q$ -Hahn Class

§18.27 $q$ -Hahn Class

… ►The $q$ -hypergeometric OP’s comprise the

q

-Hahn class (or

q

-linear lattice class) OP’s and the Askey–Wilson class (or

q

-quadratic lattice class) OP’s (§18.28). … ►There are 18 families of OP’s of

q

-Hahn class. … ►

From Big $q$ -Jacobi to Jacobi

… ►

Limit Relations

…

20: 28.36 Software

… ►For another listing of Web-accessible software for the functions in this chapter, see GAMS (class C17). …