Show that the complex potential f (z) = U∞ [z + (a/4) coth(π z /a)] represents flow

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Show that the complex potential f (z) = U∞ [z + (a/4) coth(π z /a)] represents flow past an oval shape placed midway between two parallel walls y = ±a/2. What is a practical application?

y = a/2 y = -a'2
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