07/01/2010, 10:06 PM

(07/01/2010, 09:39 AM)bo198214 Wrote:(06/28/2010, 11:18 PM)tommy1729 Wrote: (question 1)

does the following hold :

d f^n / d x^n sexp(slog(x) + k) > 0 for all positive integer n and all positive real k ?

Though tempting for uniqueness this seems not to be the case, the half iterate of exp(x)-1 (which is conjugate to ) has the following powerseries coefficients at 0:

Code:`0, 1, 1/4, 1/48, 0, 1/3840, -7/92160, 1/645120,...`

i meant for bases > sqrt(e).