Perhaps a new series for log^0.5(x) - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- 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