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

2013/09/04 by J. K. Langley, Langley, J. K., John Rossi +1
Mathematics · #30D20 #30D35 #30J99 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:30D20 #msc:30D35 #msc:30J99

paper · pdf · doi:10.48550/arxiv.1309.0927

arxiv created 2013/09/04 · arxiv updated 2013/09/05

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.

Related

• Estimation for the logarithmic partial derivative and Wiman-Valiron theory in several complex variables
• Valiron's construction in higher dimension
• A note on the Wiman-Valiron inequality
• Elementary considerations for classes of meromorphic univalent functions
• The work of Walter Bergweiler in value distribution of meromorphic functions