On the derivatives of composite functions

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

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24265:527423

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24265:527423

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Abstract

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.

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Official URL:

http://nzjm.math.auckland.ac.nz/index.php/On_the_D...

Uncontrolled Keywords:

01 Mathematical Sciences

Page Range:

57-61

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Article

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