the normalization is not a problem. Dear Suominen, than you for the try, 
but this was not the point.

Sympy uses the unitary, ordinary-frequency inverse Fourier transform and 
there should be not 1/2pi.

The problem is much deeper; that final result (without the normalization) 
is different from the theoretical result when the assumption Re[lambda]>0 
or Re[lambda]<0 and t>0 or t<0 are used.

Hope for help.

On Tuesday, April 10, 2018 at 1:44:29 PM UTC+2, Kalevi Suominen wrote:
> There are two common definitions of inverse Fourier transform depending on 
> how the frequency variable is interpreted. (See 
> The 
> stackexchange post is using the angular frequency ω that differs by the 
> factor 2π from frequency variable assumed by SymPy. The transforms are also 
> differently normalized. That may explain the differing results.
> Kalevi Suominen
> On Tuesday, April 10, 2018 at 9:16:57 AM UTC+3, Janko Slavič wrote:
>> I am trying to replicate this:
>> with sympy.
>> With Mathematica I get just the same behavior as the above theory 
>> suggest. 
>> With sympy I it looks wrong. At t<0, I get the result close to the 
>> correct one for t>0. (I was not able to include all the assumptions in 
>> sympy).
>> Here is the sympy code:
>> import sympy as sym
>> sym.init_printing()
>> ω = sym.symbols('omega', real=True, positive=True) 
>> R, λ = sym.symbols('R, lambda', complex=True)
>> t = sym.symbols('t', real=True, positive=True)
>> α = R/(sym.I*ω-λ)+sym.conjugate(R)/(sym.I*ω-sym.conjugate(λ))
>> α
>> sym.inverse_fourier_transform(α, ω, -t)
>> and the Mathematica:
>> a = InverseFourierTransform[ R/(I omega - lambda) +  Conjugate[R]/(I 
>> omega - Conjugate[lambda]), omega, t,
>>   FourierParameters -> {1, -1}]
>> Simplify[a, {Re[lambda] < 0, t > 0}]
>> Is the sympy result really wrong?

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