O14-923
> restart:

> f:=x->tan(tanh(x))-tanh(tan(x));evalf(f(2));

                f := x -> tan(tanh(x)) - tanh(tan(x))


                             2.415688672

> series(f(x),x=0,31);

        7    26   11    345584    15     551666    19
  2/45 x  - ---- x   - --------- x   + ---------- x   +
            4725       638512875       6512831325

          12676251734     23      20851369159402     27      31
        ---------------- x   - -------------------- x   + O(x  )
        2143861251406875       48076088562799171875

> f:=x->x+a*x^3+b*x^5+c*x^7:g:=x->x+d*x^3+e*x^5+h*x^7:series(f(g(x))-g(f(x)),x=0,8);

                  2                        2            7      9
     (a (3 e + 3 d ) + 5 b d - d (3 b + 3 a ) - 5 e a) x  + O(x )

> A:=3+i*x:B:=3+j*x:simplify(series((A^B-B^A)/(A-B),x=0,2));

                        (27 - 27 ln(3)) + O(x)

>