What type of singularity does $\exp(\frac{t}{2} (z - \frac{1}{z}))$ have on $z = 0, \infty$ for a fixed $t$? I've concluded this function has simple poles on both $z=0, \infty$ because I thought the function goes to infinity as it approaches to each of those singularity. But I've seen somewhere that they are essential singularities. Which is correct and why?
What type of singularity does $\exp(\frac{t}{2} (z - \frac{1}{z}))$ have on $z = 0, \infty$?
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complex-analysis
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1Related: http://math.stackexchange.com/questions/206245/singularities-of-ez-frac1z/206251#206251 – 2012-11-09