Hi, I have a function:

F[z_, d_] :=(1 + 1 / z) * (z + d /(d - 1)) / Sqrt[z + 1] / (Sqrt[z] * Sqrt[z + 1] + Sqrt[d] / (d - 1));

which (when considered as a function of a real variable z, with a real parameter d>0, d!=1) is not defined for z=d/(1-d), but has an identical limit when z = d/(1-d) is approached from both sides of the point. The values of F[z,d] can be real or imaginary, depending on z and d. The command:

Limit[F[x, d], {x → d / (1 - d)}, Direction → -1, Assumptions → {x ∈ Reals, d > 0, d ≠ 1}]

returns the correct limit, which is 2/(1+d)/Sqrt[1/(1-d)]. Note that for d>1 this limit is imaginary. However, the command

Limit[F[x, d], {x → d / (1 - d)}, Direction → 1, Assumptions → {x ∈ Reals, d > 0, d ≠ 1}]

returns incorrectly zero. Why this happens, and how can I obtain the correct limit? I would also be glad to obtain the limits in the case of complex z:

Limit[F[d / (1 - d)+i*y, d], {y → 0}, Direction → 1, Assumptions → {y ∈ Reals, d > 0, d ≠ 1}]
Limit[F[d / (1 - d)+i*y, d], {y → 0}, Direction → -1, Assumptions → {y ∈ Reals, d > 0, d ≠ 1}]

which should be different in some cases (there is a branch cut for F[z,d] along the part of the negative real axis), but the latter commands again do not seem to work correctly.
Lesław