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Obtain the Fermi function by comparing with the Bose-Einstein function

  1. Mar 20, 2014 #1
    1. The problem statement, all variables and given/known data
    Hey guys,

    So here's what we have:

    Bose-Einstein function
    [itex]g_{v}(z)=\frac{1}{\Gamma(z)}\int_{0}^{\infty}\frac{x^{v-1}dx}{z^{-1}e^{x}-1}[/itex]

    Fermi function
    [itex]f_{v}(z)=\frac{1}{\Gamma(z)}\int_{0}^{\infty}\frac{x^{v-1}dx}{z^{-1}e^{x}+1}[/itex]

    And we have the series version of the Bose-Einstein function:

    [itex]g_{v}(z)=\sum_{n=1}^{\infty}\frac{z^{n}}{n^v}[/itex]

    So by comparing the definitions of f and g, i have to find a similar series expansion for f.

    2. Relevant equations

    Given in the question!

    3. The attempt at a solution

    No idea where to start..i need a hint!!
     
  2. jcsd
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