sin ( cot 1/z) is an example of a function having infinitely many essential singularities with a limit point at z=0. It is an easy matter to give examples of elementary functions whose singularities have a countable number of limit points.
elementary
[H]e saw that the fires scattered all over the massive camp were emitting greasy fumes from the carcasses of the burning animals spitted over the flames.
Mars in the middle of the shining shield / Is grav'd, and strides along the liquid field.
blind buds
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