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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    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.

    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: 31 Jul 2020 13:45
    URI: http://shura.shu.ac.uk/id/eprint/24265

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