Table30=Table[{(m/30),((Length[IntegerPartitions[30,{m}]])/(PartitionsP[30]))}, {m,1,30}];

Fig30=ListPlot[Table30, PlotStyle->Red]

Table50=Table[{(m/50),((Length[IntegerPartitions[50,{m}]])/(PartitionsP[50]))}, {m,1,50}];

Fig50=ListPlot[Table50, PlotStyle->Blue]

Table70=Table[{(m/70),((Length[IntegerPartitions[70,{m}]])/(PartitionsP[70]))}, {m,1,70}];

Fig70=ListPlot[Table70, PlotStyle->Black]

Show[Fig30,Fig50,Fig70]

Table30a=Table[{(m/70),((Length[IntegerPartitions[30,{m}]])/(PartitionsP[30]))}, {m,1,30}];
Table50a=Table[{(m/70),((Length[IntegerPartitions[50,{m}]])/(PartitionsP[50]))}, {m,1,50}];
Table70a=Table[{(m/70),((Length[IntegerPartitions[70,{m}]])/(PartitionsP[70]))}, {m,1,70}];

Fig30a=ListPlot[Table30a, PlotStyle->Red];
Fig50a=ListPlot[Table50a, PlotStyle->Black];
Fig70a=ListPlot[Table70a, PlotStyle->Blue];

Show[Fig30a,Fig50a,Fig70a]

Hyperlink["Planck Distribution","http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html"]

(ν^2)(ν/((E^(ν/kT))-1))

Series[(ν/((E^(ν/kT))-1)),{ν,0,3}]

Manipulate[Plot[(ν^2)(ν/((E^(ν/kT))-1)),{ν,.01,40}, PlotRange->{0,40}],{kT,1,3}]

D[(ν^2)(ν/((E^(ν/kT))-1)),ν]//Simplify

3((E^x)-1)-x (E^x)