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The distribution of $a$-points of an entire function

1958
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Proceedings of the American Mathematical Society
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1. Let f(z) be an entire function of order p (0p as r->c°, (1.3) rp'(r) log r->0 as r-»oo, (1.4) log Af(r,/)gfW forr^ro = rp(r) for a sequence of values of r. S. M. Shah [2] has proved the existence of a function X(r) for an entire function of lower order X (0^X<) analogous to p(r), having the following properties: (2.1) \(r) is a non-negative, continuous function of r for r = r0. (2.2) X(r) is differentiable except at isolated points at which X'(r-O) and X'(r+0) exist. (2.3) X(r)->Xasr->«.

doi:10.1090/s0002-9939-1958-0097518-6
fatcat:6vvolj6ni5fmthnj3azuae2wtm