Mizugadro, pentation, Book

[Gottfried]

Hi Dmitrii again -

thanks for your answer!

http://mizugadro.mydns.jp/t/index.php/Tetration and looked at the entry for the tetration to base b=exp(1/e). I do not understand how you arrive at the polynomials, and especially how at the set of power-series in the table with the increasing m.

Thank you Gottfried for your interest.
The coefficients in the table are calculate using the primitive fit, quick and dirty.

Well, here I not even know what you might mean with "primitive fit". Can I find this in your Tori-wiki? If I find it I'd try this using Pari/GP to see myself, trying to use greater precision, whether my approach can be finetuned to arrive at your values at all.

However, I could find the coefficients of the first row (m=0) by my standard procedure, and my method allows 12,16 or 20 correct digits for them.

Can you evaluate tetration to the complex base?

Well, this would only be the next step, I'm afraid. If I cannot reproduce your values in the simple (=real) case, why invest more work to implement the even more difficult complex bases...
My problem is, just to find some firm way whether at all, and then how, I could reproduce your easiest coefficients with the procedures of my own language. Only if this is successful I'd go further and try complex bases too. (There will still be enough work for me to understand the method for the remaining bases, where you use Cauchy-integral and Riemann-mapping: still I've not yet the slightest idea what this really and practically is and how it is implemented - I'll still have a large corpus to study ...)

(Snipping the rest of your answer here, just focusing on the first two aspects)

Kind regards -

Gottfried

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Ah, p.s.: instead of the word "preliminary" in the exp(1/e)-section - did you possibly mean "provisorical"?