difference equations

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1: 3.6 Linear Difference Equations

§3.6 Linear Difference Equations

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§3.6(ii) Homogeneous Equations

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§3.6(iv) Inhomogeneous Equations

… ►The difference equation … …

2: Simon Ruijsenaars

… ►His main research interests cover integrable systems, special functions, analytic difference equations, classical and quantum mechanics, and the relations between these areas. …

3: 2.9 Difference Equations

§2.9 Difference Equations

… ►or equivalently the second-order homogeneous linear difference equation … ►

§2.9(ii) Coincident Characteristic Values

… ►For analogous results for difference equations of the form … ►

4: 16.25 Methods of Computation

… ►There is, however, an added feature in the numerical solution of differential equations and difference equations (recurrence relations). …

5: 18.40 Methods of Computation

… ►Usually, however, other methods are more efficient, especially the numerical solution of difference equations (§3.6) and the application of uniform asymptotic expansions (when available) for OP’s of large degree. …

6: 11.13 Methods of Computation

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§11.13(v) Difference Equations

►Sequences of values of ${𝐇}_{\nu }\left(z\right)$ and ${𝐋}_{\nu }\left(z\right)$, with $z$ fixed, can be computed by application of the inhomogeneous difference equations (11.4.23) and (11.4.25). …

7: Bibliography W

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Uniform asymptotic expansion of $J_{\nu }(\nu a)$ via a difference equation. Numer. Math. 91 (1), pp. 147–193.

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External Links:

ISSN 0029-599X, Document, MathReview (J. P. Singhal), ZentralBlatt

Referenced by:

§10.20(ii).

Encodings:

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Asymptotic expansions for second-order linear difference equations with a turning point. Numer. Math. 94 (1), pp. 147–194.

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External Links:

ISSN 0029-599X, Document, MathReview (Sergey M. Zagorodnyuk), ZentralBlatt

Referenced by:

§2.9(iii).

Encodings:

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Linear difference equations with transition points. Math. Comp. 74 (250), pp. 629–653.

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External Links:

ISSN 0025-5718, Document, MathReview (B. G. Pachpatte), ZentralBlatt

Referenced by:

§2.9(iii).

Encodings:

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Asymptotic expansions for second-order linear difference equations. II. Stud. Appl. Math. 87 (4), pp. 289–324.

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External Links:

ISSN 0022-2526, MathReview (Shao Zhu Chen), ZentralBlatt

Referenced by:

§2.9(ii).

Encodings:

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Asymptotic expansions for second-order linear difference equations. J. Comput. Appl. Math. 41 (1-2), pp. 65–94.

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External Links:

ISSN 0377-0427, Document, MathReview (Shao Zhu Chen), ZentralBlatt

Referenced by:

§2.9(i), §2.9(ii).

Encodings:

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8: 24.4 Basic Properties

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§24.4(i) Difference Equations

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9: Bibliography Z

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Doron Zeilberger’s Maple Packages and Programs Department of Mathematics, Rutgers University, New Jersey.

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Notes:

Includes hypergeometric and $q$-hypergeometric summation, solution of difference equations (for example, by Petkovšek’s algorithm), combinatorial algorithms, and (package LUC) evaluation of zonal polynomials.

External Links:

Home Page

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index, L. Lapointe and L. Vinet (1996).

Encodings:

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Error bounds for asymptotic solutions of second-order linear difference equations. J. Comput. Appl. Math. 71 (2), pp. 191–212.

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External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§2.9(i), §2.9(ii).

Encodings:

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10: Bibliography O

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Inverse factorial-series solutions of difference equations. Proc. Edinb. Math. Soc. (2) 47 (2), pp. 421–448.

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External Links:

ISSN 0013-0915, Document, MathReview (Niro Yanagihara), ZentralBlatt

Referenced by:

§2.9(i).

Encodings:

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Numerical solution of second-order linear difference equations. J. Res. Nat. Bur. Standards Sect. B 71B, pp. 111–129.

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External Links:

MathReview (G. N. Lance), ZentralBlatt

Referenced by:

§3.6(iv), §3.6(v).

Encodings:

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Bounds for the solutions of second-order linear difference equations. J. Res. Nat. Bur. Standards Sect. B 71B (4), pp. 161–166.

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External Links:

MathReview (C. W. Clenshaw), ZentralBlatt

Referenced by:

§2.9(i).

Encodings:

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