Liouville-Green-Olver approximations for complex difference equations
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 \(a\in \mathbb{C}\setminus (0,+\infty)\neq -1\) 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.
second-order linear difference equations
scientific article; zbMATH DE number 1271294
scientific article