Problem: InverseLaplaceTransform with unexpected result

• To: mathgroup at smc.vnet.net
• Subject: [mg106406] Problem: InverseLaplaceTransform with unexpected result
• From: Frank <wobbe at ifr.ing.tu-bs.de>
• Date: Mon, 11 Jan 2010 18:53:18 -0500 (EST)

```Any ideas why Mathematica 7.0.0 does not give the correct solution

In[1]:= ClearAll["Globalâ??*"]
\$Assumptions= Element[T1,Reals] && T1 >0 && Element[n,Integers] && n >0 ;
In[3]:= H[s_]:=s/((T2*s +1)^n)
imp[t_]:=InverseLaplaceTransform[H[s],s,t]
In[5]:= FullSimplify[LaplaceTransform[imp[t], t, s]]
Out[5]= 1/2 s (1+s T2)^-n

[

Sidenote: Seems that InverseLaplaceTransform inhibits unexpexcted factor
1/2:

In[6]:= InverseLaplaceTransform[H[s],s,t]
Out[6]= -((E^(-(t/T2)) (t/T2)^(1+n) (t+T2-n T2))/(2 t3 Gamma[n]))

]

whereas for specific n it is correct:

In[7]:= ClearAll["Globalâ??*"]
\$Assumptions= Element[T1,Reals] && T1 >0 && Element[n,Integers] && n >0 ;
In[7]:= H[s_]:=s/((T2*s +1)^n) /. n-> 5
imp[t_]:=InverseLaplaceTransform[H[s],s,t]
In[12]:= FullSimplify[LaplaceTransform[imp[t], t, s]]
Out[12]= s/(1+s T2)5