The linear approximation to 1/sqrt(3-x) at
x=0 is y=
(3-x)^(u) =
3^u (1 - x/3)^u =
3^u [1 - u (x/3) + u (u-1)/2 (x/3)^2 - u (u-1)(u-2)/6 (x/3)^3 + ....]
Insert u = -1/2 in here to obtain:
1/sqrt(3-x) =
1/sqrt(3) [1 + x/6 + x^2/24 +
5 x^3/432 + ... ]