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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
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: 11.13 Methods of Computation
§11.13(v) Difference Equations
Sequences of values of 𝐇 ν ( z ) and 𝐋 ν ( z ) , with z fixed, can be computed by application of the inhomogeneous difference equations (11.4.23) and (11.4.25). …
6: Bibliography W
  • Z. Wang and R. Wong (2002) Uniform asymptotic expansion of J ν ( ν a ) via a difference equation. Numer. Math. 91 (1), pp. 147–193.
  • Z. Wang and R. Wong (2003) Asymptotic expansions for second-order linear difference equations with a turning point. Numer. Math. 94 (1), pp. 147–194.
  • Z. Wang and R. Wong (2005) Linear difference equations with transition points. Math. Comp. 74 (250), pp. 629–653.
  • R. Wong and H. Li (1992a) Asymptotic expansions for second-order linear difference equations. II. Stud. Appl. Math. 87 (4), pp. 289–324.
  • R. Wong and H. Li (1992b) Asymptotic expansions for second-order linear difference equations. J. Comput. Appl. Math. 41 (1-2), pp. 65–94.
  • 7: 24.4 Basic Properties
    §24.4(i) Difference Equations
    8: Bibliography Z
  • Zeilberger (website) Doron Zeilberger’s Maple Packages and Programs Department of Mathematics, Rutgers University, New Jersey.
  • J. M. Zhang, X. C. Li, and C. K. Qu (1996) Error bounds for asymptotic solutions of second-order linear difference equations. J. Comput. Appl. Math. 71 (2), pp. 191–212.
  • 9: Bibliography O
  • A. B. Olde Daalhuis (2004a) Inverse factorial-series solutions of difference equations. Proc. Edinb. Math. Soc. (2) 47 (2), pp. 421–448.
  • F. W. J. Olver (1967a) Numerical solution of second-order linear difference equations. J. Res. Nat. Bur. Standards Sect. B 71B, pp. 111–129.
  • F. W. J. Olver (1967b) Bounds for the solutions of second-order linear difference equations. J. Res. Nat. Bur. Standards Sect. B 71B (4), pp. 161–166.
  • 10: Bibliography G
  • W. Gautschi (1997b) 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.
  • J. S. Geronimo, O. Bruno, and W. Van Assche (2004) 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.
  • V. I. Gromak (1975) Theory of Painlevé’s equations. Differ. Uravn. 11 (11), pp. 373–376 (Russian).
  • V. I. Gromak (1976) The solutions of Painlevé’s fifth equation. Differ. Uravn. 12 (4), pp. 740–742 (Russian).
  • V. I. Gromak (1987) Theory of the fourth Painlevé equation. Differ. Uravn. 23 (5), pp. 760–768, 914 (Russian).