relation to Racah polynomials

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1: 18.38 Mathematical Applications

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2: 18.28 Askey–Wilson Class

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§18.28(viii) $q$-Racah Polynomials

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3: 16.4 Argument Unity

… ►Also see Wilf and Zeilberger (1992a, b) for information on the Wilf–Zeilberger algorithm which can be used to find such relations. … ► ►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. … ►One example of such a three-term relation is the recurrence relation (18.26.16) for Racah polynomials. … …

4: Joris Van der Jeugt

… ►His research interests are in the following areas: Group theoretical methods in physics; Representation theory of Lie algebras, Lie superalgebras and quantum groups with applications in mathematical physics; 3$nj$-symbols and their relations to special functions and orthogonal polynomials; Quantum theory, finite quantum systems, quantum oscillator models, Wigner quantum systems; and Parabosons, parafermions and generalized quantum statistics. … ►As postdoc he went to Queen Mary College (London) and to the University of Southampton. … ►His results for Lie superalgebra representations continue to inspire many scientists. His publications on Clebsch-Gordan coefficients, Racah coefficients, 3$nj$-coefficients and their relation to hypergeometric series are considered as standard and a review is part of the volume on Multivariable Special Functions in the ongoing Askey–Bateman book project. …

5: 18.26 Wilson Class: Continued

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§18.26(i) Representations as Generalized Hypergeometric Functions and Dualities

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Racah $\to$ Dual Hahn

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Racah $\to$ Hahn

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§18.26(iv) Generating Functions

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Racah

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6: 37.3 Triangular Region with Weight Function

… ►They form an orthogonal basis of ${𝒱}_n^{\alpha ,\beta ,\gamma }$: … ►The coefficients in these expressions are ${}_4{}^{}F_3^{}$ hypergeometric functions that can be written in terms of Racah polynomials, see (Dunkl, 1984, Theorem 1.7) and (Iliev and Xu, 2017, Proposition 4.2). … ►

§37.3(vi) Multi-term Relations

►The three-term relations (37.2.7) give rise to a three-term and a nine-term relation as follows: … ►More generally, the polynomials (37.2.16) satisfy recurence relations of the form (37.3.30) and (37.3.32), see (Koornwinder, 1975c, §3.7.2).

7: 37.14 Orthogonal Polynomials on the Simplex

§37.14 Orthogonal Polynomials on the Simplex

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§37.14(ii) Jacobi Polynomials on the Simplex

… ►For general $d$ there is the explicit formula … ►When the permutation is cyclic, the connection coefficients that appear in expressing the new basis in terms of the basis in (37.14.7), are given by Racah polynomials of $d-1$ variables, as shown in Iliev and Xu (2017). … ►

Biorthogonality Relation

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8: null

error generating summary

9: Bibliography C

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Asymptotic behaviour of the zeros of the (generalized) Laguerre polynomial $L_n^{\alpha }(x)$ as the index $\alpha \to \mathrm{\infty }$ and limiting formula relating Laguerre polynomials of large index and large argument to Hermite polynomials. Lett. Nuovo Cimento (2) 23 (3), pp. 101–102.

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External Links:

ISSN 0024-1318, Document, MathReview (R. A. Askey)

Referenced by:

§18.7(iii).

Encodings:

BibTeX

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Asymptotics of Racah coefficients and polynomials. J. Phys. A 32 (3), pp. 537–553.

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External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§34.8, §34.8.

Encodings:

BibTeX

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On the zeros of the Askey-Wilson polynomials, with applications to coding theory. SIAM J. Math. Anal. 18 (1), pp. 191–207.

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External Links:

ISSN 0036-1410, Document, MathReview (Mourad E. H. Ismail), ZentralBlatt

Referenced by:

§18.38(iii).

Encodings:

BibTeX

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An Introduction to Orthogonal Polynomials. Mathematics and its Applications, Vol. 13, Gordon and Breach Science Publishers, New York.

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External Links:

ISBN 0-677-04150-0, MathReview (A. G. Law), ZentralBlatt

Referenced by:

§1.16(ix), (18.2.33), (18.2.36), (18.2.38), §18.2(v), §18.2(iii), §18.2(iv), §18.2(vii), §18.2(x), §18.20(i), (18.30.25), §18.30(ii), §18.30, §18.40(ii), Ch.18.

Encodings:

BibTeX

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Performance evaluation of programs related to the real gamma function. ACM Trans. Math. Software 17 (1), pp. 46–54.

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External Links:

ISSN 0098-3500, Document, MathReview, ZentralBlatt

Referenced by:

§5.24(ii), §5.24(iii).

Encodings:

BibTeX

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10: 18.21 Hahn Class: Interrelations

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§18.21(ii) Limit Relations and Special Cases

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Hahn $\to$ Jacobi

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Meixner $\to$ Laguerre

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Charlier $\to$ Hermite

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Meixner–Pollaczek $\to$ Laguerre

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