Generalized functions and integral transforms
- To: mathgroup at smc.vnet.net
- Subject: [mg34338] Generalized functions and integral transforms
- From: Name <mee at home.com.redline.ru>
- Date: Wed, 15 May 2002 03:35:39 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Tanh[y]-
LaplaceTransform[InverseLaplaceTransform[Tanh[y],y,x],x,y]//
Simplify
Out[1]=
-1
Where does it go wrong?
Doing it step by step:
InverseLaplaceTransform[Tanh[y], y, x]
Out[2]=
2*Sum[(-1)^K$144*DiracDelta[2*K$144 - x], {K$144, 0, Infinity}]
LaplaceTransform[(-1)^K$144*DiracDelta[2*K$144 - x], x, y]
Out[3]=
((-1)^K$144*UnitStep[2*K$144])/E^(2*K$144*y)
Why everything works as expected if we set UnitStep[0]==1/2?