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Liouville-Green-Olver approximations for complex difference equations. (English) Zbl 0918.39002
The authors obtain the Liouville-Green-Olver approximations for second-order linear difference equations with complex coefficients, viz., $$\Delta^2 y_n+ (a+g_n)y_n= 0,$$ when $a\in \bbfC\setminus (0,+\infty)\ne -1$ and $\sum_{n=\nu}^\infty | g_n|< \infty$. Second-order asymptotics with bounds is also obtained. The special case of ultraspherical functions of the second kind is discussed in detail.

39A11Stability of difference equations (MSC2000)
33C75Elliptic integrals as hypergeometric functions
Full Text: DOI
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