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21: Bibliography B

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Formal Power Series and Algebraic Combinatorics. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 24, American Mathematical Society, Providence, RI.

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ISBN 0-8218-0324-7, MathReview, ZentralBlatt

Referenced by:

§26.19.

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Discrete ordinate solution of Fokker-Planck equations with non-linear coefficients. Phys. Rev. A 31 (3), pp. 1855–1868.

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Referenced by:

§18.39(iii).

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Discrete ordinate solution of a Fokker-Planck equation in laser physics. Transport Theory Statist. Phys. 15 (1-2), pp. 181–210.

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Referenced by:

§18.39(iii).

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Discrete Cosine and Sine Transforms. General Properties, Fast Algorithms and Integer Approximations. Elsevier/Academic Press, Amsterdam.

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ISBN 978-0-12-373624-6; 0-12-373624-2, MathReview (Gerd Teschke)

Referenced by:

§18.3.

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22: Bibliography Z

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A proof of Andrews’ $q$-Dyson conjecture. Discrete Math. 54 (2), pp. 201–224.

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ISSN 0012-365X, Document, MathReview (Ira Gessel), ZentralBlatt

Referenced by:

§17.14.

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23: Bibliography R

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Handbook of Discrete and Combinatorial Mathematics. CRC Press, Boca Raton, FL.

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External Links:

ISBN 0-8493-0149-1, MathReview, ZentralBlatt

Referenced by:

§26.1, §26.1, §26.11, §26.19, Ch.26, Notations, Notations.

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24: 18.28 Askey–Wilson Class

… ►The Askey–Wilson polynomials form a system of OP’s $\{p_n(x)\}$, $n=0,1,2,\mathrm{\dots }$, that are orthogonal with respect to a weight function on a bounded interval, possibly supplemented with discrete weights on a finite set. … ►More generally, if $|ab|\le 1$ instead of $|a|,|b|\le 1$, discrete terms need to be added to the right-hand side of (18.28.8); see Koekoek et al. (2010, Eq. (14.8.3)). … ►Leonard (1982) classified all (finite or infinite) discrete systems of OP’s $p_n(x)$ on a set $\{x(m)\}$ for which there is a system of discrete OP’s $q_m(y)$ on a set $\{y(n)\}$ such that $p_n(x(m))=q_m(y(n))$. …

25: 28.12 Definitions and Basic Properties

… ►For given $\nu$ (or $\cos \left(\nu \pi \right)$) and $q$, equation (28.2.16) determines an infinite discrete set of values of $a$, denoted by ${\lambda }_{\nu +2n}\left(q\right)$, $n=0,\pm 1,\pm 2,\mathrm{\dots }$. …

26: Bibliography K

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Jacobi polynomials, Bernstein-type inequalities and dispersion estimates for the discrete Laguerre operator. Adv. Math. 333, pp. 796–821.

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ISSN 0001-8708, Document, Link, MathReview (Martin Axel Hallnäs)

Referenced by:

§18.14(i).

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27: Bibliography L

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Discrete-variable representations and their utilization. In Advances in Chemical Physics, pp. 263–310.

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External Links:

ISBN 9780470141731, Document, Link

Referenced by:

§18.38(i).

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28: 3.7 Ordinary Differential Equations

… ►If $q(x)$ is $C^{\mathrm{\infty }}$ on the closure of $(a,b)$, then the discretized form (3.7.13) of the differential equation can be used. …

29: 18.2 General Orthogonal Polynomials

… ►If the orthogonality discrete set $X$ is $\{0,1,\mathrm{\dots },N\}$ or $\{0,1,2,\mathrm{\dots }\}$, then the role of the differentiation operator $d/dx$ in the case of classical OP’s (§18.3) is played by ${\mathrm{\Delta }}_x$, the forward-difference operator, or by ${\nabla }_x$, the backward-difference operator; compare §18.1(i). … ►In further generalizations of the class $𝒮$ discrete mass points $x_k$ outside $[-1,1]$ are allowed. … ►If $d\mu \in 𝐌(a,b)$ then the interval $[b-a,b+a]$ is included in the support of $d\mu$, and outside $[b-a,b+a]$ the measure $d\mu$ only has discrete mass points $x_k$ such that $b\pm a$ are the only possible limit points of the sequence $\{x_k\}$, see Máté et al. (1991, Theorem 10). …

30: Bibliography W

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On the connection formulas of the third Painlevé transcendent. Discrete Contin. Dyn. Syst. 23 (1-2), pp. 541–560.

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External Links:

ISSN 1078-0947, Document, MathReview (Galina V. Filipuk), ZentralBlatt

Referenced by:

§32.13(ii).

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