Re: does it make sense ? The conditional

• To: mathgroup at smc.vnet.net
• Subject: [mg107624] Re: [mg107608] does it make sense ? The conditional
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Sat, 20 Feb 2010 06:37:13 -0500 (EST)
• References: <201002190835.DAA00933@smc.vnet.net>

```michael partensky wrote:
> In   =   md[t] = Integrate[Exp[t u^(1/2 ) - u/2], {u, 0, \[Infinity]}]
> Out =  If[Re(t)<0,Sqrt[2 \[Pi]] E^(t^2/2) t
> (erf(t/Sqrt[2])+1)+2,Integrate[E^(t
> Sqrt[u]-u/2),{u,0,\[Infinity]},Assumptions->Re(t)>=0]]
> However,
> In =    md[t] - Integrate[Exp[t u^(1/2 ) - u/2], {u, 0, \[Infinity]},
>  Assumptions -> Re[t] < 0]
> Out = Sqrt[2 \[Pi]] E^(t^2/2) t (erf(t/Sqrt[2])+1)+2
> In =    md[t] - Integrate[Exp[t u^(1/2 ) - u/2], {u, 0, \[Infinity]},
>  Assumptions -> Re[t] > 0]
> Out = Sqrt[2 \[Pi]] E^(t^2/2) t (erf(t/Sqrt[2])+1)+2
>
> Why doesn't yellow output contain the same analytical expression  for both
> the assumptions (or just one analytical expression)?
> I thought that the original expression is returned only when the analytical
> result does not exist. What am I missing?
> Thanks. Michael.

Which one is the "yellow" output?

What do you mean by returning "the original expression"? I see nothing
to indicate the situation I would have taken that to indicate.

What version of Mathematica are you using? In 7.0.1 I do not see the
same results for the inputs you indicate.

Daniel Lichtblau
Wolfram Research

```

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