# Series around a point

I have the function Vt

Vn = (-G*Mn)/Sqrt[x^2 + y^2 + z^2 + cn^2];
Vd = (-G*Md)/Sqrt[x^2 + y^2 + (s + Sqrt[h^2 + z^2])^2];
Vb = (G*Mb)/(2*a)*(ArcSinh[(x - a)*(y^2 + z^2 + c^2)^(-1/2)] -
ArcSinh[(x + a)*(y^2 + z^2 + c^2)^(-1/2)]);
Vh = (-G*Mh)/Sqrt[x^2 + y^2 + z^2 + ch^2];
Vrot = -(Ωb^2/2)*(x^2 + y^2);

Vt = Vn + Vd + Vb + Vh + Vrot;

G = 1; Mn = 400; cn = 0.25;
Md = 7000; s = 3; h = 0.175;
Mb = 3500; a = 10; c = 1;
Mh = 20000; ch = 20;
Ωb = 4.5;


and I want to expand it in a series around P(x0,0,0), where x0 = 10.63695596. The output should be of the form

V = V(x0,0,0) - A (x - x0)^2 /2 + B y^2 / 2 + C z^2 /2


where V(x0,0,0) = -3242.772174938595.

Any ideas how to get this? It must be very simple.

• Look up Series. – march Nov 20 '15 at 16:55
• @march I looked the documentation but it does not contain any relevant examp0le on expansion around a 3D point. – Vaggelis_Z Nov 20 '15 at 16:57
• I'm pretty sure it's the second use-case listed at the top of the Series documentation page. – march Nov 20 '15 at 16:58
• @march But the output it's not in the desired form. – Vaggelis_Z Nov 20 '15 at 16:59

   se[n_Integer, x0_:1] :=

• If the point is P(x0,0,0) how would be the general code? – Vaggelis_Z Nov 20 '15 at 17:27