A new characterisation of the Eremenko-Lyubich class

J. Anal. Math. 123, 1 (2014), 95–105. Also available on the arXiv.The Eremenko-Lyubich class of transcendental entire functions with a bounded set of singular values has been much studied. We give a new characterisation of this class of functions. We also give a new result regarding direct singularities which are not logarithmic.