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does it make sense ? The conditional

• To: mathgroup at smc.vnet.net
• Subject: [mg107608] does it make sense ? The conditional
• From: michael partensky <partensky at gmail.com>
• Date: Fri, 19 Feb 2010 03:35:31 -0500 (EST)

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.

• Follow-Ups:
  • Re: does it make sense ? The conditional
    • From: Daniel Lichtblau <danl@wolfram.com>