how to do the equation following its answer on matlab?

after solving this equation how can i verify or compute the answer on matlab??

Answer 1

[John D'Errico]

There is the obvious...

Using y = 1/z, we can transform the problem.

syms z y
Fz = (1/z + 1/z^2 - 1/z^3)/(1 + 1/z + 1/z^2 + 4/z^3);

Fy = subs(Fz,z,1/y);

Ty = taylor(Fy,y,'order',7)
Ty =
6*y^6 + 4*y^5 - 2*y^4 - 2*y^3 + y

Tz = subs(Ty,y,1/z)
Tz =
1/z - 2/z^3 - 2/z^4 + 4/z^5 + 6/z^6