FullSimplify
only simplifies the result of the following calculation halfway, leaving a lot of $e^{x^2/v}$ and $e^{m^2/v}$ terms that could have been cancelled:
gau[x_, v_] = (1/Sqrt[2*Pi*v])*E^-((x^2)/(2*v));
f[x_] = gau[x - m, v]/2 + gau[x + m, v]/2;
FullSimplify[D[Log[f[x]], {v, 4}]]
I tried combinations of Simplify
, FullSimplify
, Expand
, and PowerExpand
, and the cancellations don't happen.
Question 1: How can I make it to those cancellations? Ultimately I'd like the entire expression with all the $e^{n\ x/v}$ replaced with $y^n$, but that's the next step after I solve this current problem.
Question 2: Maybe this is a Meta question, but is there a page somewhere (on this site or elsewhere) on tricks and hacks for simplifying expressions that Mathematica built-ins don't nail? Or just how to get the simplifying juuuust the way you want it? Controlling simplification and more complete simplification seem to be a recurring themes in SE questions. Could such a page be started on SE if it doesn't already exist?