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Zeta function for Debye Low Temp. Limit

  1. Mar 22, 2013 #1
    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. jcsd
  3. Mar 22, 2013 #2
    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.
     
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