(* plna *)

f1=Integrate[x BesselJ[0,β x],{x,0,1}]

f1=f1/Limit[f1,β->0]

p1=Plot[f1,{β,0,15},PlotStyle->Black,PlotRange->All]

(* gaussovska apod - soucet rady *)

Integrate[Exp[-x^2] BesselJ[0, x] x,{x,0,1}]

α=2;f2g=Table[Sum[BesselJ[m,β]2^(m-1)α^(2m-2)/β^m,{m,1,n}],{n,1,10,2}];

f2gnorm=f2g/(f2g/.β->0.001);

Plot[f2gnorm,{β,0,15},PlotRange->All]

(* kvadraticka apod *)

apod=(1-x^2)

Plot[apod,{x,-1,1}]

f2=Integrate[apod x BesselJ[0,β x],{x,0,1}]

f2=f2/Limit[f2,β->0]

p2=Plot[f2,{β,0,15},PlotStyle->Red,PlotRange->All]

Show[{p1,p2}]

(* kvadraticka inverzni apod *)

invapod=x^2

Plot[invapod,{x,-1,1}]

f3=Integrate[invapod x BesselJ[0,β x],{x,0,1}]

f3=f3/Limit[f3,β->0]

p3=Plot[f3,{β,0,15},PlotStyle->Green,PlotRange->All]

Show[{p1,p3}]

Show[{p1,p2,p3}]

(* uzavrena energie *)

tot1=Integrate[β f1^2,{β,0,r},Assumptions->r>0]

tot1=tot1/Integrate[β f1^2,{β,0,Infinity}]

p1b=Plot[tot1,{r,0,15},PlotStyle->Black,PlotRange->All]

tot2=Integrate[β f2^2,{β,0,r},Assumptions->r>0]

tot2=tot2/Integrate[β f2^2,{β,0,Infinity}]

p2b=Plot[tot2,{r,0,15},PlotStyle->Red,PlotRange->All]

tot3=Integrate[β f3^2,{β,0,r},Assumptions->r>0]

tot3=tot3/Integrate[β f3^2,{β,0,Infinity}]

p3b=Plot[tot3,{r,0,15},PlotStyle->Green,PlotRange->All]

Show[{p1b,p2b,p3b}]