Taylor series of cheta

[Sergo]

How can it help me to evaluate 3[0.5]3 and 3[1.5]3?

Hello there, Xorter, to calculate hyperops with fractional ranks, you can use PARI/GP, and kneser.gp, plus small code which uses cheta function for that.

First, download PARI/GP: http://pari.math.u-bordeaux.fr/download.html
Then, download kneser.gp: http://math.eretrandre.org/tetrationforu...hp?tid=486
And finally, download attachment from my post.

After installation of PARI/GP, put kneser.gp and hyper.gp in the same folder as PARI/GP's (gp.exe), then drag'n'drop hyper.gp onto gp.exe, and it will start both kneser.gp and hyper.gp.
Now you will be able to calculate all you want, but be aware, that I've shifted original hyperops by one, so addition is [1], instead of [0] (you can change it back in the code).

To calculate a[s]b in PARI/GP now, you only need to write

Code:

h(a,s,b)

and that's all. Also, this code allows you to calculate some roots:

Code:

hr(a,s,b)

For example: h(2,3,5) = 32, hr(32,3,5)=2