07/09/2018, 08:34 PM

Hi!

I agree with Sheldon almost at all. If I were you, I would use the following notations:

Hn(a,b) = a[n]b = H(a,n,b) or the Knuth's uparrows, the second is simplest as I think.

If you want iterate an operator, just use the following functional power formula:

y [z+1] x = (y [z] x)^o(y-1) o y

I suppose that z can be negative, zero, rational, real or complex, too.

But if you follow Sheldon's zeration formula, it will not lead to addition, so I think that is wrong.

But Sheldon has a lot of successful pari/gp programme and ideas for the realizations of from the tetration to heptation, but hard to interpolate with rational or real numbers.

Good luck!

Xorter

I agree with Sheldon almost at all. If I were you, I would use the following notations:

Hn(a,b) = a[n]b = H(a,n,b) or the Knuth's uparrows, the second is simplest as I think.

If you want iterate an operator, just use the following functional power formula:

y [z+1] x = (y [z] x)^o(y-1) o y

I suppose that z can be negative, zero, rational, real or complex, too.

But if you follow Sheldon's zeration formula, it will not lead to addition, so I think that is wrong.

But Sheldon has a lot of successful pari/gp programme and ideas for the realizations of from the tetration to heptation, but hard to interpolate with rational or real numbers.

Good luck!

Xorter

Xorter Unizo