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This provides an effective means for computing the index.
By relatively straightforward means one can show that ......
Then $F$ and $G$ are homotopic by means of a homotopy $H$ such that ......
It is easy to see, by means of an example, that ......
Find integral formulas by means of which the coefficients $c_n$ can be computed from $f$.
The difficulty is that it is by no means clear what one should mean by a normal family.
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