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Question: Digamma and Polygamma Functions Question

Question:Digamma and Polygamma Functions Question

dcasimir 1212
February 13 2008
0

rho[nu] = 4*Pi/(h^3)*Int(x^3/(exp(x/(k*T))+1), x = 0..infinity)

How can I show that the above integral equals 75*Pi^5*(k*T)^4/(30*h^3)

 

This is from Arfken's Math Methods for Physicists in Chapter 8.2, on the Digamma and Polygamma functions.

Please help,

getting frustrated,

 

very respectfully,

 

 
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