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Re: FullSimplify with Pi

• To: mathgroup at smc.vnet.net
• Subject: [mg84132] Re: [mg84129] FullSimplify with Pi
• From: Carl Woll <carlw at wolfram.com>
• Date: Tue, 11 Dec 2007 06:06:46 -0500 (EST)
• References: <200712110320.WAA26066@smc.vnet.net>

Uberkermit wrote:

>Greetings,
>
>I would like to simplify an expression involving Pi. Actually,
>simplifying the expression isn't hard, getting Mathematica to
>recognize the simplification is the hard part. Consider:
>
>Assuming[Element[x, Reals],
>  FullSimplify[Log[1/Sqrt[2 Pi] Exp[x]]]]
>
>Mathematica doesn't do anything to simplify this. However, replacing
>the symbol Pi with any other variable in the above leads to the
>trivial substitutions.
>
>By trivial, I mean:
> Log[Exp[x]] = x, and Log[a/b] = Log[a] - Log[b].
>
>Why does Pi confuse Mathematica so??
>
>Thanks,
>-Chris
>  
>
Use PowerExpand:

In[111]:= PowerExpand[Log[1/Sqrt[2 Pi] Exp[x]],
 Assumptions -> Element[x, Reals]]

Out[111]= x+1/2 (-log(2)-log(\[Pi]))

Carl Woll
Wolfram Research

• References:
  • FullSimplify with Pi
    • From: Uberkermit <chris.r.sims@gmail.com>