Re: Different results with FourierTransform[]

*To*: mathgroup at smc.vnet.net*Subject*: [mg97616] Re: [mg97588] Different results with FourierTransform[]*From*: Richard Hofler <rhofler at bus.ucf.edu>*Date*: Tue, 17 Mar 2009 04:58:20 -0500 (EST)*References*: <200903160924.EAA25551@smc.vnet.net>

Hello Wieland, It appears that the answer you get depends on when the replacement rule B -> 1 is evaluated. In[4]:= sol1 = InverseFourierTransform[Tanh[x],x,p] Out[4]= -(I/(2 p Sqrt[2 \[Pi]]))-3/4 I Sqrt[\[Pi]/2] Csch[(p \[Pi])/2]-(5 HarmonicNumber[-(1/2)-(I p)/4])/(8 Sqrt[2 \[Pi]])-(3 HarmonicNumber[-(1/2)+(I p)/4])/(8 Sqrt[2 \[Pi]])+(5 HarmonicNumber[-((I p)/4)])/(8 Sqrt[2 \[Pi]])+(3 HarmonicNumber[(I p)/4])/(8 Sqrt[2 \[Pi]]) In[5]:= sol2 = InverseFourierTransform[Tanh[B x],x,p]/.B->1 Out[5]= -I Sqrt[\[Pi]/2] Csch[(p \[Pi])/2] In[6]:= sol3 = InverseFourierTransform[Tanh[B x]/.B->1,x,p] Out[6]= -(I/(2 p Sqrt[2 \[Pi]]))-3/4 I Sqrt[\[Pi]/2] Csch[(p \[Pi])/2]-(5 HarmonicNumber[-(1/2)-(I p)/4])/(8 Sqrt[2 \[Pi]])-(3 HarmonicNumber[-(1/2)+(I p)/4])/(8 Sqrt[2 \[Pi]])+(5 HarmonicNumber[-((I p)/4)])/(8 Sqrt[2 \[Pi]])+(3 HarmonicNumber[(I p)/4])/(8 Sqrt[2 \[Pi]]) In[7]:= sol1 == sol3 Out[7]= True HTH, Richard Richard Hofler -----Original Message----- From: Wieland Brendel [mailto:wielandbrendel at gmx.net] Sent: Monday, March 16, 2009 5:25 AM To: mathgroup at smc.vnet.net Subject: [mg97616] [mg97588] Different results with FourierTransform[] Dear reader, I somewhat stumbled over the following behaviour of mathematica: I tried to calculate the fouriertransform of Tanh[x]. I did this in two ways: 1. Directly: InverseFourierTransform[Tanh[x], x, p] 2. Indirectly: InverseFourierTransform[Tanh[B x], x, p] where I set B -> 1 in the end. However, the result between the two approaches differs: Whereas in the first approach I get a complex number (with both real and imaginary part being non-zero for almost all values of p), the result in the second approach yields NO real part; the imaginary part however is the same as in the first approach. Is there any explanation for this behaviour? Thanks a lot in advance! I am really stuck with that... Wieland

**References**:**Different results with FourierTransform[]***From:*Wieland Brendel <wielandbrendel@gmx.net>