On extension to "other" iteration roots

[JmsNxn]

Very interested by your approach at solving \( b=1/2 \). It looks very much like the Kouznetsov approach--but refined slightly. Have you read Kouznetsov's book on calculating superfunctions--because you're using his notation, just curious. If you haven't it's a very good read. And definitely works very similar to what you have here.

You got me thinking about trying \( b=1/2 \) too, using infinite compositions. My solution looks similar to yours (they're not the same because the toy model I used was for a 2 pi i periodic tetration with singularities at \( \Im(s) = (2k+1) \pi \) for \( k \in \mathbb{Z} \))--but they definitely look very similar.

I hope school is going well! I'm sure, by how advanced you already are, you'll do fine!

Regards, James

Thank you, James!

Did you mean the original superfunction part? Yes I used a slightly diffenrent notation like T(z), but the rest of the post I referred to no one. Especially the P function part, which is the core of the section II.

I'm looking forward to your solution, your last beta method is very awesome!

Leo

Does the P approach generalize to other functions? I will admit I'm still a little confused by it, but it seems to be working, lol. I ask because I don't see anything too specific to tetration, so I wonder if it works in more elaborate scenarios.


regards, James