I made a similar question in the past.
Let's define the function $H_n(a,b)$ to be the $n$-th hyperoperation which imputs are $a$ and $b$.
- $H_1(a,b)= a+b~~$ Addition
- $H_2(a,b)= ab~~$ Multiplication
- $H_3(a,b)= a^b~~$ Exponentiation
- $H_4(a,b)=$ $^{b}a~~$ Tetration
I already made previous posts trying to extend these to negative integer hyperoperators.
My question here is similar : is there a way to define or calculate something like $H_i(a,b)$ where $i^2=-1$ ? The $i$-th hyperoperation.
And ideally, is there by any chance any ways to calculate the specific number $H_i(i,i)$?
$H_1(i,i)=2i$
$H_2(i,i)=-1$
$H_3(i,i)=e^{-\pi/2}≈0.2078795764$
$H_4(i,i)≈0.50012906+0.32426694i$
$H_5(i,i)=?$
$$H_i(i,i)=?$$