/sci/ - Science & Math

>>11441118
The first step into the red square is plugging in the definition, that is, introducing parenthesis because multiplication is left to right.
For the second step, we set [math]C = ((( \cdots (a_{m+1} \circ a_{m+2} ) \circ a_{m+3}) \circ \cdots ) \circ a_{n-1} )[/math] to obtain [math]B = C \circ a_n[/math], then [math]A \circ (C \circ a_n ) = (A \circ C) \circ a_n )[/math] and I think you just throw in the induction hypothesis.
Then again, I can't see the entire proof.
>>11441241
>>linear fractional function
>What? The Mobius transforms are projective, not linear.
https://en.wikipedia.org/wiki/Linear_fractional_transformation

Thank you for the question, I'll throw away some time trying to figure it out.
>>11441713
Compose the changes of variables [math](x, y) \rightarrow (r, \theta) \rightarrow (ar \cos \theta , br \sin \theta )[/math]
You should get a linear transformation. From then, it's pretty simple.