In[]:=
$Version
Out[]=
14.3.0 for Microsoft Windows (64-bit) (July 8, 2025)
In[]:=
f[t_]:=
2
Pi
*HeavisidePi[t/2]Sqrt[1-t^2]​​ft=FourierTransform[f[t],t,k,FourierParameters->{1,-1}];​​con=2InverseFourierTransform[ft^2,k,t,FourierParameters->{1,-1}]
Out[]=
-
2tMeijerG{{},{1,2}},-
1
2
,
1
2
,{},
2
t
4
(1+UnitStep[-2-t](-1+UnitStep[t])+(-2+UnitStep[-2+t])UnitStep[t])
π
In[]:=
Asymptotic[con,{t,0,1},Assumptions->t>=0]
Out[]=
32
3
2
π
In[]:=
N[%,20]
Out[]=
1.0807592921849362287
In[]:=
N[con/.t->10^-19,20]
Out[]=
1.0807592921849362287
In[]:=
f1[t_]=Piecewise[{{0,t<=-1},{(2/Pi)*(Sqrt[1-t^2]),-1<t<1},{0,t>=1}}];​​g1[t_]:=2*NIntegrate[f1[tau]*f1[t-tau],{tau,-Infinity,Infinity},WorkingPrecision->20];​​g1[0]
Out[]=
1.0807592921849362287
Plot[con,{t,-3,3}](*toomuchtimetogenerateaplot*)