difference equations
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1: 3.6 Linear Difference Equations
§3.6 Linear Difference Equations
… ►§3.6(ii) Homogeneous Equations
… ►§3.6(iv) Inhomogeneous Equations
… ►The difference equation … …2: Simon Ruijsenaars
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►His main research interests cover integrable systems, special functions, analytic difference equations, classical and quantum mechanics, and the relations between these areas.
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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
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►There is, however, an added feature in the numerical solution of differential equations and difference equations (recurrence relations).
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5: 11.13 Methods of Computation
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§11.13(v) Difference Equations
►Sequences of values of and , with fixed, can be computed by application of the inhomogeneous difference equations (11.4.23) and (11.4.25). …6: Bibliography W
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Uniform asymptotic expansion of via a difference equation.
Numer. Math. 91 (1), pp. 147–193.
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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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Linear difference equations with transition points.
Math. Comp. 74 (250), pp. 629–653.
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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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Asymptotic expansions for second-order linear difference equations.
J. Comput. Appl. Math. 41 (1-2), pp. 65–94.
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7: 24.4 Basic Properties
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§24.4(i) Difference Equations
…8: Bibliography Z
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Doron Zeilberger’s Maple Packages and Programs
Department of Mathematics, Rutgers University, New Jersey.
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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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9: 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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Numerical solution of second-order linear difference equations.
J. Res. Nat. Bur. Standards Sect. B 71B, pp. 111–129.
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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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10: Bibliography G
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The Computation of Special Functions by Linear Difference Equations.
In Advances in Difference Equations (Veszprém, 1995), S. Elaydi, I. Győri, and G. Ladas (Eds.),
pp. 213–243.
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WKB and turning point theory for second-order difference equations.
In Spectral Methods for Operators of Mathematical Physics,
Oper. Theory Adv. Appl., Vol. 154, pp. 101–138.
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Theory of Painlevé’s equations.
Differ. Uravn. 11 (11), pp. 373–376 (Russian).
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The solutions of Painlevé’s fifth equation.
Differ. Uravn. 12 (4), pp. 740–742 (Russian).
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Theory of the fourth Painlevé equation.
Differ. Uravn. 23 (5), pp. 760–768, 914 (Russian).
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