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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.

MSC:
39A11Stability of difference equations (MSC2000)
33C75Elliptic integrals as hypergeometric functions
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References:
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