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variable of integration not localized in Integrate and Sum?

• To: mathgroup at smc.vnet.net
• Subject: [mg63827] variable of integration not localized in Integrate and Sum?
• From: Don Hatch <hatch at plunk.org>
• Date: Tue, 17 Jan 2006 04:33:23 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Apparently I need to explicitly localize t in the following,
otherwise it messes up when I pass in t as the second argument.
    In:
        F[f_, x_] := Integrate[f[x + t], {t, -1/2, 1/2}]
        F[Sin, x]
        F[Sin, t]
    Out:
        2 Sin[1/2] Sin[x]  <---- correct
        0                  <---- ?!?!
This is surprising to me-- I thought that
the fact that t is the integration variable
would cause it to be automatically localized, but apparently not.
To get the right answer, I can say:
    In:
        F[f_, x_] := Module[{t}, Integrate[f[x + t], {t, -1/2, 1/2}]]
        F[Sin, x]
        F[Sin, t]
    Out:
        2 Sin[1/2] Sin[x]  <---- correct
        2 Sin[1/2] Sin[t]  <---- correct
(note, I really have to use Module, not Block-- it still messes up using
Block).

The documentation for Integrate doesn't seem to support my hope that t gets
localized, as far as I could see;
however, note that exactly the same problem
occurs for Sum, whose documentation does explicitly state:
   The iteration variable i is treated as local.
So here is an example that seems to clearly contradict the documentation
of Sum:
   In:
       F[f_, x_] := Sum[f[x + t], {t, -1/2, 1/2, 1/10}]/11
       F[Identity, x]
       F[Identity, t]
   Out:
       x              <---- correct
       0              <---- ?!?!
Just as for Integrate, it works properly when I explicitly
localize using Module (but not Block):
   In:
       F[f_, x_] := Module[{t}, Sum[f[x + t], {t, -1/2, 1/2, 1/10}]/11]
       F[Identity, x]
       F[Identity, t]
   Out:
       x              <---- correct
       t              <---- correct

Is this a bug in Sum and/or Integrate?
I'm using Mathematica version 5.2.0.0, on Linux/X.

Don Hatch

• Follow-Ups:
  • Re: variable of integration not localized in Integrate and Sum?
    • From: Pratik Desai <pdesai1@umbc.edu>
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