- #1

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If anyone could help me clarify this, I would greatly appreciate it.

Thanks

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- Thread starter kcuf
- Start date

- #1

- 6

- 0

If anyone could help me clarify this, I would greatly appreciate it.

Thanks

- #2

- 6

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also, maybe I'm just an idiot, but I how do I get this forum to display tex?

- #3

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Maybe I should clarify what's motivating this question:

I'm trying to use the Christoffel-Schwarz, and the text I have been using says that the powers are computed with respect to the principal branch, however examples that I have seen online just seem to naively combine squareroots together in order to find a potential antiderivative, for example http://planetmath.org/encyclopedia/ExampleOfSchwarzChristoffelTransformation.html [Broken]. What also troubles me with this example, is if we were restricted to the principal branch, then $\sqrt{z^2-1}$ is not analytic on the upper half plane (because it sends most of the imaginary axis to the negative real axis), so it shouldn't be an antiderivative unless we can choose a different branch for the derivative (which seems wierd), right?

I'm trying to use the Christoffel-Schwarz, and the text I have been using says that the powers are computed with respect to the principal branch, however examples that I have seen online just seem to naively combine squareroots together in order to find a potential antiderivative, for example http://planetmath.org/encyclopedia/ExampleOfSchwarzChristoffelTransformation.html [Broken]. What also troubles me with this example, is if we were restricted to the principal branch, then $\sqrt{z^2-1}$ is not analytic on the upper half plane (because it sends most of the imaginary axis to the negative real axis), so it shouldn't be an antiderivative unless we can choose a different branch for the derivative (which seems wierd), right?

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