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

Mathematica graphics

Mathematica graphics

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]

Tags:

Bugs

Complex