What properties do hyperoperations base pi have?

π+π~6.283.

π*π~9.870.

π^π~36.462.

π^^π~19,924,084,821,713,599,984,983,799,892,180,468,936,939.296.

For \(n\in\Bbb N\), is π[n]π ever an integer/rational/constructible number/algebraic?

Like before:

Also, the picture is 443 pixels by 314 pixels wide.

Using logarithmic semi-operators base the pith root of pi, π{x}π For some reason, any non real valuedness is not showing up. Isn't the analytic continuation of the Kneser method not real valued at the pith root of pi? Although, I do have some issues with tetration at base the pith root of pi.

Using logarithmic semi-operators base the pith root of pi, here is graph of \(y=\Re(\pi\{x\}\pi)\), from \(-\pi\) to \(\pi\):

π+π~6.283.

π*π~9.870.

π^π~36.462.

π^^π~19,924,084,821,713,599,984,983,799,892,180,468,936,939.296.

For \(n\in\Bbb N\), is π[n]π ever an integer/rational/constructible number/algebraic?

Like before:

Quote:The .png file attached to this post is smaller than the .txt file attached to this..

The .txt file attached might not look right on a smart phone.

The text graphs need a monospaced font.

The image attached to this post looks blurry, because of the size of the image.

Also, the picture is 443 pixels by 314 pixels wide.

Using logarithmic semi-operators base the pith root of pi, π{x}π For some reason, any non real valuedness is not showing up. Isn't the analytic continuation of the Kneser method not real valued at the pith root of pi? Although, I do have some issues with tetration at base the pith root of pi.

Using logarithmic semi-operators base the pith root of pi, here is graph of \(y=\Re(\pi\{x\}\pi)\), from \(-\pi\) to \(\pi\):

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ฅ(ﾐ⚈ ﻌ ⚈ﾐ)ฅ Sincerely: Catullus /ᐠ_ ꞈ _ᐟ\

ฅ(ﾐ⚈ ﻌ ⚈ﾐ)ฅ Sincerely: Catullus /ᐠ_ ꞈ _ᐟ\