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The Second Derivative of a Meromorphic Function of Finite Order
Author(s) -
Langley J. K.
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609302001558
Subject(s) - meromorphic function , mathematics , order (exchange) , derivative (finance) , finitely generated abelian group , complex plane , pure mathematics , plane (geometry) , function (biology) , mathematical analysis , geometry , finance , evolutionary biology , biology , financial economics , economics
Let f be meromorphic of finite order in the plane, such that the second derivative f ″ has finitely many zeros. Then f has finitely many poles. This result was conjectured by the author in 1996, and an example shows that the theorem is sharp.