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21: Tom H. Koornwinder

… ►Koornwinder has published numerous papers on special functions, harmonic analysis, Lie groups, quantum groups, computer algebra, and their interrelations, including an interpretation of Askey–Wilson polynomials on quantum SU(2), and a five-parameter extension (the Macdonald–Koornwinder polynomials) of Macdonald’s polynomials for root systems BC. …

22: Peter Paule

… ►Paule’s main research interests are computer algebra and algorithmic mathematics, together with connections to combinatorics, special functions, number theory, and other related fields. …

23: Ranjan Roy

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1 Algebraic and Analytic Methods

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24: 18.38 Mathematical Applications

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Zhedanov Algebra

… ►See Zhedanov (1991), Granovskiĭ et al. (1992, §3), Koornwinder (2007a, §2) and Terwilliger (2011). Similar algebras can be associated with all families of OP’s in the $q$-Askey scheme and the Askey scheme. … ►Algebraic structures were built of which special representations involve Dunkl type operators. In the $q$-case this algebraic structure is called the double affine Hecke algebra (DAHA), introduced by Cherednik. …

25: Roderick S. C. Wong

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1 Algebraic and Analytic Methods

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26: 28.34 Methods of Computation

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Solution of the matrix eigenvalue problem for each of the five infinite matrices that correspond to the linear algebraic equations (28.4.5)–(28.4.8) and (28.14.4). See Zhang and Jin (1996, pp. 479–482) and §3.2(iv).

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Solution of the systems of linear algebraic equations (28.4.5)–(28.4.8) and (28.14.4), with the conditions (28.4.9)–(28.4.12) and (28.14.5), by boundary-value methods (§3.6) to determine the Fourier coefficients. Subsequently, the Fourier series can be summed with the aid of Clenshaw’s algorithm (§3.11(ii)). See Meixner and Schäfke (1954, §2.87). This procedure can be combined with §28.34(ii)(d).

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27: 32.9 Other Elementary Solutions

… ►Then ${\text{P}}_{\text{III}}$ has algebraic solutions iff … ► ${\text{P}}_{\text{V}}$, with $\delta =0$, has algebraic solutions if either … ►An elementary algebraic solution of ${\text{P}}_{\text{VI}}$ is … ►Dubrovin and Mazzocco (2000) classifies all algebraic solutions for the special case of ${\text{P}}_{\text{VI}}$ with $\beta =\gamma =0$, $\delta =\frac{1}{2}$. For further examples of algebraic solutions see Andreev and Kitaev (2002), Boalch (2005, 2006), Gromak et al. (2002, §48), Hitchin (2003), Masuda (2003), and Mazzocco (2001b). …

28: 21.7 Riemann Surfaces

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§21.7(i) Connection of Riemann Theta Functions to Riemann Surfaces

… ►Belokolos et al. (1994, §2.1)), they are obtainable from plane algebraic curves (Springer (1957), or Riemann (1851)). …Equation (21.7.1) determines a plane algebraic curve in ${ℂ}^2$, which is made compact by adding its points at infinity. … ►

§21.7(iii) Frobenius’ Identity

… ►These are Riemann surfaces that may be obtained from algebraic curves of the form …

29: Bibliography K

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Gravitational field of a spinning mass as an example of algebraically special metrics. Phys. Rev. Lett. 11 (5), pp. 237–238.

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External Links:

Document, MathReview (C. Gilbert), ZentralBlatt

Referenced by:

§31.17(ii).

Encodings:

BibTeX

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Algebraic Aspects of Cryptography. Springer-Verlag, Berlin.

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Notes:

Second printing with corrections

External Links:

ISBN 3-540-63446-0, MathReview (M. V. D. Burmester), ZentralBlatt

Referenced by:

§23.20(iii).

Encodings:

BibTeX

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Orthogonal polynomials and computer algebra. In Recent developments in complex analysis and computer algebra (Newark, DE, 1997), R. P. Gilbert, J. Kajiwara, and Y. S. Xu (Eds.), Int. Soc. Anal. Appl. Comput., Vol. 4, Dordrecht, pp. 205–234.

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External Links:

FullText, MathReview Entry, ZentralBlatt

Referenced by:

CAOP (website).

Encodings:

BibTeX

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Meixner-Pollaczek polynomials and the Heisenberg algebra. J. Math. Phys. 30 (4), pp. 767–769.

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External Links:

ISSN 0022-2488, Document, MathReview, ZentralBlatt

Referenced by:

§18.21(ii).

Encodings:

BibTeX

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The relationship between Zhedanov’s algebra $\mathrm{AW}(3)$ and the double affine Hecke algebra in the rank one case. SIGMA 3, pp. Paper 063, 15 pp..

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External Links:

ISSN 1815-0659, Link, MathReview (James W. Parkinson), ZentralBlatt

Referenced by:

§18.38(iii), §18.38(iii), §18.38(iii).

Encodings:

BibTeX

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30: 15.17 Mathematical Applications

… ►These monodromy groups are finite iff the solutions of Riemann’s differential equation are all algebraic. …