Strange behavior of Limit in Mathematica 9 and 10 (bug?)
Not an answer, but possible hint as to what's going on:
Try the following in Mathematica 9 and 10.0.
(*1*) Limit[1 + Log[-a - I y], y → 0, Direction → -1, Assumptions → {a > 0}]
(* 1 + I*π + Log[a]*)
(*2*) Limit[1 + Log[-x - I y], y → 0, Direction → -1, Assumptions → {x > 0}]
(* 1 - I*π + Log[x] <-- in v9 only.*)
In v9, the one with x
is right, the one with a
(and any other letter) is wrong. Clearly, Wolfram is encouraging users to use x
as the variable.
In v10.0, Wolfram concedes, and all letters give the wrong result.
This has been fixed in 10.1 on windows:
$Version
code for the above
expr1 = Log[-m^2 - I eta];
Limit[expr1, eta -> 0, Assumptions -> m^2 > 0]
expr2 = Log[-m^2 + I eta];
Limit[expr2, eta -> 0, Assumptions -> m^2 > 0]
a + expr1;
Limit[%, eta -> 0, Assumptions -> m^2 > 0]
a + expr2;
Limit[%, eta -> 0, Assumptions -> m^2 > 0]