I have never used Mathematica before, but I am contemplating using it to solve this problem for a simple case of $f(x) = C, 1<x<2$ and $= 0$. I can easily get $\hat{f}$, the Fourier transform of $f$, without any help from Mathematica. From there, I intend to use it to verify the following statement.

$$ $$

for $a = 0,b = 3/2$.

I don't know anything about Mathematica. I would like your advice about going ahead with it. I speculate (am almost sure) there might not be any closed form expressions possible in this problem, so I am wondering if Mathematica's symbolic machinary can really crack this. Also, if one exists, I'd like to know which suitable package I need to buy.

EDIT : My effort

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I need to evaluate

Limit[V[ω]/(((log[ω])^2)*(G[ω])), ω -> Infinity]

I don't know where should I paste this code and how can I evaluate this. All the above code was pasted in a single cell. Please help me how to proceed.

Code :

f[x_] := Piecewise[{{0,x<=1},{C,1<x<2},{0,x>=2}}]
ft[ω_] := FourierTransform[f(x),x,ω]
L[t_,ω_]:=Integrate[ft[α] Exp[I α t],{α,0,ω}, Assumptions->ω>0]
Lbar[t_,ω_] := Conjugate[L[t,ω]]
K[t_,ω_] := Integrate[L[t,α]*Lbar[t,α]*Abs[ft[α]],{α,0,ω}, Assumptions->ω>0]
P[t_,ω_] := Integrate[L[t,α]*Abs[ft[α]],{α,0,ω}, Assumptions->ω>0]
M[t_,ω_] := Integrate[Lbar[t,α]*Abs[ft[α]],{α,0,ω}, Assumptions->ω>0]
G[ω_] := Integrate[Abs[ft[α]],{α,0,ω}, Assumptions -> ω>0]
SI[t_,ω_] := K[t,ω] - ((1/G[ω])*P[t,ω]*M[t,ω])
dSI[t_,ω_] := D[SI[t,ω],t]
V[ω_] := Integrate[Abs[dSI[t,ω]],{t,0,3}, Assumptions->ω>0]
B[C] := Limit[V[ω]/(((log[ω])^2)*(G[ω])),ω->Infinity]
  • $\begingroup$ Can't you just do Simplify[Limit[] == Sum[]]? $\endgroup$ – Feyre Dec 31 '16 at 11:56
  • $\begingroup$ @Feyre : Did you go through the entire problem? I get to the expression under the limit, after evluating several integrals. What you are saying is only the final step. $\endgroup$ – Rajesh Dachiraju Dec 31 '16 at 11:59
  • $\begingroup$ You're right, if it's a more extensive problem you should show what you have done so far yourself though. $\endgroup$ – Feyre Dec 31 '16 at 12:00
  • $\begingroup$ @Feyre : The problem is essentially evaluating definite integrals and finally the limit. I have no acquaintance with mathematica and I need help to begin with and want toknow if its even doable. I have just downloaded mathematica trial version. Any tips to begin with? $\endgroup$ – Rajesh Dachiraju Dec 31 '16 at 12:02
  • $\begingroup$ So say, defining your function L with L[t_, \[Omega]_] := Integrate[ft[\[Alpha]] Exp[I \[Alpha] t], {\[Alpha], 0, \[Omega]}, Assumptions -> \[Omega] > 0] when ft is your fourier transformed function. Then you can call L[t, \[Alpha]]? $\endgroup$ – Feyre Dec 31 '16 at 12:15

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