I have
$$ f(x) = \sqrt{\ln\left(a\cosh^{2}(mx)(1+bx^{2})\right)} $$
If I expand this as a series I should get something of the form
$$ \sqrt{\ln a}+gx^{2}+\mathcal{O}(x^{4}) $$
but I'm having real difficulty getting Mathematica to give me the necessary Taylor series of $f(x)$. Can anyone help? I only really need $g$, the later coefficients aren't necessary. Perhaps there's a reason why Mathematica has a problem?