continuous Hahn polynomials

SearchAdvancedHelp

(0.004 seconds)

11—13 of 13 matching pages

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

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

►Ismail (1986) gives asymptotic expansions as $n\to \mathrm{\infty }$, with $x$ and other parameters fixed, for continuous $q$-ultraspherical, big and little $q$-Jacobi, and Askey–Wilson polynomials. …For Askey–Wilson $p_n(\cos \theta ;a,b,c,d|q)$ the leading term is given by … ►For a uniform asymptotic expansion of the Stieltjes–Wigert polynomials, see Wang and Wong (2006). ►For asymptotic approximations to the largest zeros of the $q$-Laguerre and continuous $q^{-1}$-Hermite polynomials see Chen and Ismail (1998).

12: 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

… ►

Limit Relations

…

13: 18.38 Mathematical Applications

… ►

Approximation Theory

… ►

Integrable Systems

… ►The $3j$ symbol (34.2.6), with an alternative expression as a terminating ${}_3{}^{}F_2^{}$ of unit argument, can be expressed in terms of Hahn polynomials (18.20.5) or, by (18.21.1), dual Hahn polynomials. The orthogonality relations in §34.3(iv) for the $3j$ symbols can be rewritten in terms of orthogonality relations for Hahn or dual Hahn polynomials as given by §§18.2(i), 18.2(iii) and Table 18.19.1 or by §18.25(iii), respectively. … …