we can get the continued fraction of cot(x) with the command

> convert(cot(x), confrac, x, 6)

the result is

(1+x^2/(-3+x^2/(5-(1/7)*x^2)))/x

how could I convert this result to a form like

1/x-(1/10)*x+49*x/(20*x^2-210)

the calculation is like the following command, the result in the picture

restart;
with(VectorCalculus);
SetCoordinates(spherical[r, theta, phi]);
Fv := rho*VectorField(`<,>`(v[r](r, theta, phi), v[theta](r, theta, phi), v[phi](r, theta, phi)));
Divergence();
Divergence(Fv);

1) when the Divergence act on the Fv, then it will be expanded, which is lengthy and not like most book's formulation , especially when I want to continue for a Conversation law like in fluid mechanics, this will be too long and a messy for later check.

could there be a way to not expand this result, just as the eq(3) like.

2) when I want to calculate the Divergence of Fv, I must construct a VectorField at first, but this is in components way, is there a quick way for Vector Field Function

we always have subscript variable in the math book, but how could this be natral done in maple

I want to get a seq a₁ a₂ a₃

seq(a[i],i=1..3)

but how could I get a  a_ij

seq(a[i_j],i=1..3);

and

seq(a[ij],i=1..3);  both was not right