Liouville-Green-Olver approximations for complex difference equations
type: Item
instance of: scholarly article
title: Liouville-Green-Olver approximations for complex difference equations
zbMATH Open document ID: 0918.39002
author: Marco Vianello
author: Francesca Locatelli
author: Renato Spigler
published in: Journal of Approximation Theory
publication date: 1999-08-19T00:00:00Z
review text: 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.
reviewed by: R. P. Agarwal
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 33C75
zbMATH DE Number: 1271294
zbMATH Keywords: Liouville-Green-Olver approximations
zbMATH Keywords: second-order linear difference equations
zbMATH Keywords: complex coefficients
zbMATH Keywords: asymptotics
zbMATH Keywords: ultraspherical functions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1271294