? BesselJ

Plot[Table[BesselJ[m,x],{m,0,5}],{x,0,10}]

Plot[{BesselJ[0,x],BesselJ[1,x],BesselJ[2,x],BesselJ[3,x],BesselJ[4,x],Sqrt[2/Pi/x]Cos[x-Pi/4],Sqrt[2/Pi/x]Sin[x-Pi/4]},{x,0,20}]

BesselJ[0,0]

p0=Plot[Table[BesselJZero[0,n],{n,1,3}],{x,0,1},Axes->False];
p1=Plot[{BesselJZero[1,1]},{x,1,2}];
Show[p0,p1,PlotRange->{0,10},Frame->True]

Show[Table[Plot[Table[BesselJZero[m,n],{n,1,3}],{x,m-.3,m+.3},Axes->False],{m,0,3}],PlotRange->{0,10},Frame->True]