Hi everyone,
I'm trying to find a function of single variable f(x) with the following properties:
-It is symmetric around zero
-It is differentiable everywhere
-f'(x)≥0 for all x>0
-f'(x)=0 when x=0
-f'(x)≤0 for all x<0
(I think these last two actually follow from the first three?)...
Hi, a naive question here, but I was wondering if the series
\sum^{∞}_{k=0} k a^{k}
has a particular name? As in 'geometric series' for \sum^{∞}_{k=0} a^{k} ?
And what about the more general \sum^{∞}_{k=0} k^{n} a^{k} ?
As a related question, you seem to be able to get the formula for the...
This is actually related to a post I made earlier in the differential equations forums, but I've since realized that solving the equations themselves is not necessarily the best way to get where I want to go. Perhaps it's better suited to this forum, since it is an integration problem that I...
I've been trying to figure out how to integrate 1/(x+ln(x)) but am not getting anywhere. Mathematica can't do it, and I haven't found it in lists of integrals.
Does anyone know if this integral exists in closed form?
Same goes for (x+ln(x))/(1+x+ln(x))
Thanks!
zeroseven
Hi everyone, new member zeroseven here. First, I want to say that it's great to have a forum like this! Looking forward to participating in the discussion.
Anyway, I need to solve a pair of differential equations for an initial value problem, but am not sure if an analytical solution exists. I...