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Hyper-Operations, Base Pi
#1
Question 
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.
Is π[n]π ever an integer/rational/constructible number/algebraic, for [Image: gif.image?\dpi%7B110%7Dn\in\mathbb%7BN%7D]?
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=π{x}π from -π to π:


Attached Files Image(s)
   

.txt   Y=π{x}π.txt (Size: 1.71 KB / Downloads: 47)
ฅ(ミ⚈ ﻌ ⚈ミ)ฅ
Please remember to stay hydrated.
Sincerely: Catullus
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#2
Catullus, be clearer. What is this a graph of?

You write \(\pi[x]\pi\). What does that mean? Please work better. Explain better.
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#3
(06/24/2022, 08:41 AM)JmsNxn Wrote: Catullus, be clearer. What is this a graph of?

You write \(\pi[x]\pi\). What does that mean? Please work better. Explain better.
It is a graph of y=exp^(x-1)(log^(x-1)(π)+log^(x-1)(π)), for log and exp base [Image: gif.image?\dpi%7B110%7D\sqrt%5B\pi%5D%7B\pi%7D] with the analytic continuation of the Kneser method.
ฅ(ミ⚈ ﻌ ⚈ミ)ฅ
Please remember to stay hydrated.
Sincerely: Catullus
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