0
Since z = a^2/z on the circle, we see that w as given by (1) is purely
real on the circle C and therefore if* = 0. Thus C is a streamline.
If the point z is outside 0, the point az
/z is inside 0, and vice-versa. Since
all the singularities off(z) are by hypothesis exterior to C, all the singularities
off(a?/z) are interior to C ; in particular f(a
z
/z) has no singularity at infinity,
since f(z) has none at z = 0. Thus w has exactly the same singularities as/(z)
and so all the conditions are satisfied.
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∙ 13y ago
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Parts of formal proof of theorem?
Parts of formal proof of theorem?
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