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Mathematica confusion


Thanks to the many people who have responded to my earlier posting.
Let me see if I can be more clear, and refrain from embarassing
myself further.

When I enter the expression

      (1/x) (1/x^2)^(1/x^2 -1)

mma simplifies it to

      x^(-1 - 2 (-1 + x^(-2)))

Now, consider x = -2 (not -1 as I mistyped previously). In the first
expression, x is squared before any roots are taken, so it is natural
to expect a real answer. In the second case, a root of -2 is taken and
a complex answer is no surprise. mma's simplification effects the
choice of the branch cut.

This is not a bug. The question of branch cuts is difficult. Instead,
let me post this as a query - how can I get mma to take the cut I
want? Note that mma is not entirely consistent on this point:

      (1/x) (1/x^2)^(1/x^2 -1) /. x-> -2
and
      f[x_] := (1/x) (1/x^2)^(1/x^2 -1)
      f[-2]

return different answers.

                               E. Neely Atkinson
                               AN123651 at UTHVM1.BITNET
                               neely at mdaali.cancer.utexas.edu


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