On the derivatives of composite functions

LINGHAM, Eleanor and LANGLEY, James K (2007). On the derivatives of composite functions. New Zealand Journal of Mathematics, 36, 57-61.

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Let g be a non-constant polynomial and let f be transcendental and meromorphic of sub-exponential growth in the plane. Then if k\geq 2 and Q is a polynomial the function (f\circ g)^{(k)}-Q has infinitely many zeros. The same conclusion holds for k \geq 0 and with Q a rational function if f has finitely many poles. We also show by example that this result is sharp.

Item Type: Article
Uncontrolled Keywords: 01 Mathematical Sciences
Page Range: 57-61
SWORD Depositor: Symplectic Elements
Depositing User: Symplectic Elements
Date Deposited: 31 Jul 2020 13:45
Last Modified: 17 Mar 2021 23:49
URI: https://shura.shu.ac.uk/id/eprint/24265

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