Hahn polynomials

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11: 18.38 Mathematical Applications

… ►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. … …

12: 18.29 Asymptotic Approximations for $q$-Hahn and Askey–Wilson Classes

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

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13: Bibliography K

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The Hahn polynomials, formulas and an application. Scripta Math. 26, pp. 33–46.

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External Links:

MathReview (L. J. Slater), ZentralBlatt

Referenced by:

§18.20(i), §18.21(ii), §18.26(ii).

Encodings:

BibTeX

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Clebsch-Gordan coefficients for $\mathrm{SU}(2)$ and Hahn polynomials. Nieuw Arch. Wisk. (3) 29 (2), pp. 140–155.

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External Links:

ISSN 0028-9825, MathReview (Jiří Patera), ZentralBlatt

Referenced by:

§18.38(iii).

Encodings:

BibTeX

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Orthogonal polynomials with weight function ${(1-x)}^{\alpha }{(1+x)}^{\beta }+M\delta (x+1)+N\delta (x-1)$ . Canad. Math. Bull. 27 (2), pp. 205–214.

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External Links:

ISSN 0008-4395, MathReview (Wolfgang Hahn), ZentralBlatt

Referenced by:

§18.36(i), §18.36(i).

Encodings:

BibTeX

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14: 13.6 Relations to Other Functions

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Charlier Polynomials

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15: 18.2 General Orthogonal Polynomials

… ►This happens, for example, with the continuous Hahn polynomials and Meixner–Pollaczek polynomials (§18.20(i)). … ►In fact, these are the only OP’s which are Sheffer polynomials (with Krawtchouk polynomials being only a finite system) …

16: Bibliography

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Continuous Hahn polynomials. J. Phys. A 18 (16), pp. L1017–L1019.

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External Links:

ISSN 0305-4470, FullText, MathReview (T. S. Chihara), ZentralBlatt

Referenced by:

§18.19, §18.20(ii), §18.21(ii).

Encodings:

BibTeX

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17: Bibliography L

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Global asymptotics of the Hahn polynomials. Anal. Appl. (Singap.) 11 (3), pp. 1350018, 47.

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External Links:

ISSN 0219-5305, Document, FullText, MathReview (Yamilet Quintana), ZentralBlatt

Referenced by:

§18.24, §18.24.

Encodings:

BibTeX

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18: 15.9 Relations to Other Functions

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Krawtchouk

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19: 16.4 Argument Unity

… ►The characterizing properties (18.22.2), (18.22.10), (18.22.19), (18.22.20), and (18.26.14) of the Hahn and Wilson class polynomials are examples of the contiguous relations mentioned in the previous three paragraphs. …

20: 18.15 Asymptotic Approximations

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§18.15(i) Jacobi

… ►See Hahn (1980), where corresponding results are given when $x$ is replaced by a complex variable $z$ that is bounded away from the orthogonality interval $[-1,1]$. … ►

§18.15(ii) Ultraspherical

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§18.15(iii) Legendre

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§18.15(iv) Laguerre

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