> (I don't know how to make Maxima expand sinh(x) in terms of
> exponentials, without doing the same for sin(x)).
To do this, substitute a lambda form for sinh:
(%i3) sin(x) * sinh(x^2 + y^2)$
(%i4) subst(lambda([s], exp(s) / 2 - exp(-s)/2), sinh, %);
(%o4) sin(x)*(%e^(y^2+x^2)/2-%e^(-y^2-x^2)/2)
Or if you like
(%i5) subst(lambda([s], exponentialize(sinh(s))), sinh, %o3);
(%o5) (sin(x)*(%e^(y^2+x^2)-%e^(-y^2-x^2)))/2
Barton