Assume that has a power-series representation in terms of powers of , verify that it has the form

for real with .

We know that for we have the following expansions

Then we have

This was the requested identity.

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Stumbling Robot

A Fraction of a Dot
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Verify that *log ((1+x) / (1-x))*^{1/2} = ∑ x^{2n+1} / (2n+1)

Assume that has a power-series representation in terms of powers of , verify that it has the form

for real with .

We know that for we have the following expansions

Then we have

This was the requested identity.