quotient-difference scheme

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21: Bibliography D

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Unification of one-dimensional Fokker-Planck equations beyond hypergeometrics: Factorizer solution method and eigenvalue schemes. Phys. Rev. E (3) 57 (1), pp. 252–275.

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External Links:

ISSN 1063-651X, Document, MathReview (Victor I. Stepanov), ZentralBlatt

Referenced by:

§31.17(ii).

Encodings:

BibTeX

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22: Bibliography L

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Orthogonal polynomials, duality and association schemes. SIAM J. Math. Anal. 13 (4), pp. 656–663.

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External Links:

ISSN 0036-1410, Document, MathReview (C. L. Parihar), ZentralBlatt

Referenced by:

§18.28(viii), §18.28(xi), §18.38(iii).

Encodings:

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23: 3.8 Nonlinear Equations

… ►After a zero $\zeta$ has been computed, the factor $z-\zeta$ is factored out of $p(z)$ as a by-product of Horner’s scheme (§1.11(i)) for the computation of $p(\zeta )$. …

24: Bibliography C

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Work Group of Computational Mathematics, University of Kassel, Germany.

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Notes:

Computer Algebra and Orthogonal Polynomials: a Web service using Maple for online generation of formulas and graphs of orthogonal polynomials belonging to the Askey scheme. For further information see Swarttouw (1997) and Koepf (1999).

External Links:

CAOP

Referenced by:

1st item.

Encodings:

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A dispersion analysis for difference schemes: Tables of generalized Airy functions. Math. Comp. 32 (144), pp. 1163–1170.

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External Links:

ISSN 0025-5718, FullText, MathReview (Philip Brenner), ZentralBlatt

Referenced by:

§9.13(ii).

Encodings:

BibTeX

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25: 18.26 Wilson Class: Continued

… ►Moreover, if one or more of the new parameters becomes zero, then the polynomial descends to a lower family in the Askey scheme.

26: Bibliography B

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Algebraic Combinatorics. I: Association Schemes. The Benjamin/Cummings Publishing Co., Inc., Menlo Park, CA.

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External Links:

ISBN 0-8053-0490-8, MathReview Entry, ZentralBlatt

Referenced by:

§18.28(xi).

Encodings:

BibTeX

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27: 2.7 Differential Equations

… ►To include the point at infinity in the foregoing classification scheme, we transform it into the origin by replacing $z$ in (2.7.1) with $1/z$; see Olver (1997b, pp. 153–154). …

28: 18.39 Applications in the Physical Sciences

… ►Following the method of Schwartz (1961), Yamani and Reinhardt (1975), Bank and Ismail (1985), and Ismail (2009, §5.8)  have shown this is equivalent to determination of $x$ such that $c_N(x)=0$ in the recursion scheme …

29: Errata

… ►These additions were facilitated by an extension of the scheme for reference numbers; with “_” introducing intermediate numbers. … ►

The unnumbered equation

$$\underset{c\to -n}{lim}\frac{F(a,b;c;z)}{\mathrm{\Gamma }\left(c\right)}=𝐅(a,b;-n;z)=\frac{{\left(a\right)}_{n+1}{\left(b\right)}_{n+1}}{(n+1)!}{z}^{n+1}F(a+n+1,b+n+1;n+2;z),$$ $n=0,1,2,\mathrm{\dots }$

was added in the second paragraph. An equation number will be assigned in an expanded numbering scheme that is under current development. Additionally, the discussion following (15.2.6) was expanded.

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