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 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 |