In a comment in MSE a contributor proposes a formula for the half-logarithm (log^°0.5(x)) see the comments here:

https://math.stackexchange.com/questions...53_1272791
I proposed to the author to discuss it on our forum or on the sandbox of the MSE-network. Everyone interested is invited to take a look at it.

Gottfried

This is a joke right ?

If not remember that an infinite series of elementary functions is usually equal to a truncated finite sum of that series + the error term ... where the error term is usually also either very small or also elementary !!

This implies that already a finite amount of terms added is already a good approximation OR the special part is in the error term.

But when i see error terms smaller than log for the half-iterate of log , I get “ suspicious “.

Hence forgive my rude reaction.

Ofcourse if the coefficients are nontrivial we might do better , but in that case we probably get some self-reference and things like “ fake-function theory “.

Regards

Tommy1729

On the other hand I should perhaps thank you because now people might start to see the relevance of fake function theory.

Regards

Tommy1729