I am curious if this is covered in any textbooks or papers. I am interested in finding out how to solve functional and differential (even pde) equations involving power towers in them. For example if tow(f(x),n)= g(x) where tow meant a diagonal power tower of f with n determining it's height. Also, can this be solved if some of the f's in the tower (not necessarily all of them) were derivatives , or even partial derivatives in a multivariable case? I'm also interested in what happens if n goes to infinity. Thanks.
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Do you mean things like $f(x)^{(f(x)^{f(x)})}$ ? (parentheses are important). IMHO, these are very artificial constructions that haven't much interest... – Jean Marie Sep 03 '21 at 09:20
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Yes, I'd still like to know if there is something out there. – James Shelton Sep 03 '21 at 19:57