Rational sums of inverse powers of fixed points of e

[jaydfox]

The first one looks about right, meaning it looks familiar at a glance.

Hmm, going through Excel, the next few look correct, so at least we're on the same page there.

Now, to get the first sum, we'll sum the inverse 2nd powers. To start, square each of the values you listed:

Code:

-0.472565386708 - 0.238338175183*I
-0.013946445102 - 0.008184595884*I
-0.004613490799 - 0.001820881553*I
-0.002277041586 - 0.000693879494*I
-0.001352042857 - 0.000339668175*I
-0.000894117468 - 0.000192447243*I

And of course, we'll add the conjugates as well. Essentially then, just double the real parts and sum them.

The second sum is the sum of the inverse 3rd powers, so cube the values you listed and sum (including conjugates).