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+--- Thread: Perhaps a new series for log^0.5(x) (/showthread.php?tid=1243)
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
RE: Perhaps a new series for log^0.5(x) - Daniel - 03/21/2020
I added an answer to https://math.stackexchange.com/questions/1269643/continuum-between-addition-multiplication-and-exponentiation.
Daniel