13 citations · 14 across the 13 of their papers we have counts for
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Asymptotic values, deficiencies and Bank-Laine functions
J. K. Langley
Some results are proved concerning asymptotic and deficient values in connection with the second order linear differential equation , in which the coefficient is…
Non-real zeros of derivatives in the unit disc
James Langley
The main result establishes an estimate for the growth of a real meromorphic function on the unit disc such that: (i) at least one of and has finitely many poles…
Non-real zeros of derivatives
J. K. Langley
A number of results are proved concerning non-real zeros of derivatives of real meromorphic functions. In particular, the paper supersedes the previous arXiv submission "Non-real z…
Bank-Laine functions with real zeros
J. K. Langley
Every real Bank-Laine function of finite order, whose zeros are all real but neither bounded above nor bounded below, either has an explicit representation in terms of trigonometri…
Transcendental singularities for a meromorphic function with logarithmic derivative of finite lower order
J. K. Langley
In this note it is shown that two key results on transcendental singularities for meromorphic functions of finite lower order have refinements which hold under the weaker hypothesi…
Linear differential polynomials in zero-free meromorphic functions
J. K. Langley
The paper determines all meromorphic functions with finitely many zeros in the plane having the property that a linear differential polynomial in the function, of order at least 3…
Trajectories escaping to infinity in finite time
J. K. Langley
If the function is transcendental and meromorphic in the plane, and either has finitely many poles or its inverse function has a logarithmic singularity over infinity, then…
Non-real zeros of derivatives of meromorphic functions
J. K. Langley
A number of results are proved concerning non-real zeros of derivatives of real and strictly non-real meromorphic functions in the plane
Wiman-Valiron theory for a class of functions meromorphic in the unit disc
J. K. Langley, John Rossi
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 Stal…
The Schwarzian derivative and the Wiman-Valiron property
J. K. Langley
Suppose that a transcendental meromorphic function in the plane has finitely many critical values, while its multiple points have bounded multiplicities, and its inverse function h…
Derivatives of meromorphic functions of finite order
J. K. Langley
A result is proved concerning meromorphic functions of finite order in the plane such that all but finitely many zeros of the second derivative are zeros of the first derivative.
Non-real zeros of derivatives of real meromorphic functions
J. K. Langley
The main result of the paper determines all real meromorphic functions of finite order in the plane for which the first derivative has finitely many zeros, while the function itsel…
Baker domains for Newton's method
Walter Bergweiler, D. Drasin, J. K. Langley
We show that there exists an entire function without finite asymptotic values for which the associated Newton function tends to infinity in some invariant domain. The question whet…