# Zeta function for Debye Low Temp. Limit

1. Mar 22, 2013

### phys_student1

Hello,

In the low temp. limit of Debye law for specific heat, we encounter the following integral:

∫(x4 ex)/(ex-1)2 dx, from 0 to ∞.

The result is 4∏2/15.

I have searched and found this to be related to zeta function but zeta functions do not have ex in the numerator so I am unable to evaluate the integral using them.

Any help?

2. Mar 22, 2013

### phys_student1

Never mind. I found that what should be integrated is the energy, ∫x3/(ex-1) which can be integrated easily using integration by parts then using zeta function, the result is π2/15.