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 Perhaps a new series for log^0.5(x) Gottfried Ultimate Fellow Posts: 795 Threads: 121 Joined: Aug 2007 12/05/2019, 04:35 PM 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 Gottfried Helms, Kassel tommy1729 Ultimate Fellow Posts: 1,507 Threads: 358 Joined: Feb 2009 02/17/2020, 10:51 PM 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 tommy1729 Ultimate Fellow Posts: 1,507 Threads: 358 Joined: Feb 2009 02/17/2020, 10:57 PM On the other hand I should perhaps thank you because now people might start to see the relevance of fake function theory. Regards  Tommy1729 Daniel Fellow Posts: 95 Threads: 33 Joined: Aug 2007 03/21/2020, 08:28 AM I added an answer to https://math.stackexchange.com/questions...nentiation. Daniel « Next Oldest | Next Newest »

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