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Perhaps a new series for log^0.5(x) - Printable Version

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Perhaps a new series for log^0.5(x) - Gottfried - 12/05/2019

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/1269643/continuum-between-addition-multiplication-and-exponentiation/1272791?noredirect=1#comment7121653_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


RE: Perhaps a new series for log^0.5(x) - tommy1729 - 02/17/2020

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


RE: Perhaps a new series for log^0.5(x) - tommy1729 - 02/17/2020

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

Regards 

Tommy1729