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 Thanks in advance, Frank