# difference equations

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## 1—10 of 95 matching pages

##### 1: 3.6 Linear Difference 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 DifferenceEquations
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 equations3.6) and the application of uniform asymptotic expansions (when available) for OP’s of large degree. …
##### 6: 11.13 Methods of Computation
###### §11.13(v) DifferenceEquations
Sequences of values of $\mathbf{H}_{\nu}\left(z\right)$ and $\mathbf{L}_{\nu}\left(z\right)$, with $z$ fixed, can be computed by application of the inhomogeneous difference equations (11.4.23) and (11.4.25). …
##### 7: Bibliography W
• Z. Wang and R. Wong (2002) Uniform asymptotic expansion of $J_{\nu}(\nu a)$ 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.
##### 9: 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.
• ##### 10: 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.