Corrigendum to "An infinite family of bounds on zeros of analytic functions and relationship to Smale's bound"

(2) |ξ − ξ′| ≥ rm γm(ξ′) . If we assume that ξ′ is also a simple root, then clearly a symmetry argument also proves the inequality (1) and, hence, the present proof remains valid. But this added assumption is unnecessary. To correct the proof of Theorem 3.2 essentially all that is needed is to switch ξ and ξ′; i.e., assume that ξ′ is a simple root while relaxing the simplicity assumption on ξ. Except possibly for a finite set of values of z, the following expansion formula, given as equation (2.7) in [1], is valid even when ξ is not a simple root of f(z):