Wiman-Valiron theory for a class of functions meromorphic in the unit disc

Langley, James; Rossi, John

Abstract

Analogues of the key results of Wiman-Valiron theory are proved for a class of functions meromorphic in the unit disc, based on an approach developed by Bergweiler, Rippon and Stallard for the plane setting. The results give local approximations for the function and its logarithmic derivative and, in the case of positive order of growth, for higher order logarithmic derivatives as well.

Citation

Langley, J., & Rossi, J. (2014). Wiman-Valiron theory for a class of functions meromorphic in the unit disc. Mathematical Proceedings of the Royal Irish Academy, 114A(2), https://doi.org/10.3318/pria.2014.114.14

• Journal Article Type: Article
• Acceptance Date: Jan 8, 2014
• Publication Date: Jul 15, 2014
• Deposit Date: Jul 5, 2018
• Print ISSN: 1393-7197
• Publisher: Royal Irish Academy
• Peer Reviewed: Peer Reviewed
• Volume: 114A
• Issue: 2
• DOI: https://doi.org/10.3318/pria.2014.114.14
• Public URL: https://nottingham-repository.worktribe.com/output/1101319
• Publisher URL: https://www.jstor.org/stable/10.3318/pria.2014.114.14#metadata_info_tab_contents