symbolizing an undefined function like f(x)=(((x)^x)^x)......upto infinity

[shubhankarsharma00]

I found no way to symbolize an infinite series like the one in the issue above.

[asmeurer]

This is tetration, which can be represented using the Knuth up arrow. It isn't implemented in SymPy, though it could be. I wonder what sorts of things could be computed with it, though. Is there a closed form for the derivative?

[asmeurer]

It also would probably help to have some kind of BigNumber implementation first (see #6835).

[shubhankarsharma00]

I am new here and was just going through sympy docs and I thought of the issue. I dont have any specific use for it in mind, though if we can't write this expression in sympy it won't be possible to find it's derivattive or perform other functions on it like in this example : https://math.stackexchange.com/questions/1317314/derivative-of-xxx-to-infinity

[sidhantnagpal]

Actually, I dont think the link you mentioned is the same thing as the one posted here mainly because exponentiation follows right to left associativity.
So, in general, a**b**c != ((a)**b)**c.
As @asmeurer mentioned, tetration (Knuth up arrow notation) would be useful only if we strip the expression of braces.
Further (the expression without braces), could be written as an implicit function y=x***y for the evaluation of derivatives.