Logarithm reciprocal

[Gottfried]

Perhaps we can relate this to Euler's "false logarithmic series"

which is that formula?

Hmm, maybe best is to read the article. The formula is on page 2 and 3.
Euler's "false logarithmic series" (Ed Sandifer)

I've found the taylor-expression of the truncations of this series when I interpolated 2^0,2^1,2^2,2^3,... polynomially (*1) ...
But anyway - I still don't know whether this can be related to your problem here, so ...

Gottfried

(*1) or was it this "exponential polynomial interpolation"? don't have it exactly in mind - I had a certain question and tried with a lot of options recently without archiving all the partial successes and failings. I'll see whether I can reproduce it