Gamma Function

Table[Gamma[n],{n,1,10}]

Show[
Plot[Gamma[x],{x,-3,5},PlotRange->{-10,25}],
ListPlot[Table[{n,(n-1)!},{n,1,5}],PlotStyle->Orange]
]

Bessel Functions

Plot[BesselJ[0,z],{z,0,20}]

bjs=Table[BesselJ[m,z],{m,0,6}]
Plot[bjs,{z,0,30}]

Table[BesselJZero[1,n],{n,1,5}]//N

bys=Table[BesselY[m,z],{m,0,6}]
Plot[bys,{z,0,30}]

Table[BesselYZero[1,n],{n,1,5}]//N

Illustrate Orthogonality

z[m_,n_]:=N[BesselJZero[m,n]]

m=0
NIntegrate[BesselJ[m,z[m,3]*r]*BesselJ[m,z[m,17]*r]*r,{r,0,1}]

Plot[{BesselJ[m,z[m,3]*r],BesselJ[m,z[m,7]*r]},{r,0,20}]