## Interesting Integral

**Problem:** Compute

**Solution:** First note that

But, since for every we have that we see that

Now, using the fact that a power series is uniformly convergent on it’s disk of convergence it follows that

So, letting we see that

And thus remembering the definition of this becomes

To compute this sum we note that (ignoring convergence issues)

which upon inspection is equal to

Thus, solving for the desired sum we get that

So, finally

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