On extension to "other" iteration roots

[JmsNxn]

I would say the only disparaging fact about this expansion is that if you are going to expand in \(s\) (if we want the multiplier to be locally holomorphic) we'd have to be more clever. I think it would make sense to generalize this to \(s^x \theta_s(x)\) to try and get holomorphy in \(s\), which shouldn't be too hard if you fiddle around.

Don't let yourself be fooled by \(|s|\) it actually just means \(-s\), its more to make it clear that \(-s\) is positive!

Yes, I was fooled at first; but then it clicked.