Solving Fermi-Dirac Integral: Step-by-Step Guide

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Discussion Overview

The discussion centers around the Fermi-Dirac integral and its expansion using Taylor series. Participants express confusion regarding the integral's representation and seek clarification on the steps involved in its derivation.

Discussion Character

  • Homework-related, Technical explanation, Exploratory

Main Points Raised

  • One participant expresses confusion about the integral in their textbook related to Fermi-Dirac statistics and requests help in understanding the expansion.
  • The integral presented involves a function of u, denoted as ⌽(u), and is evaluated from 0 to ∞, with specific conditions on uf.
  • Another participant requests that mathematical expressions be formatted in LaTeX for clarity.
  • A third participant attempts to provide assistance but does not elaborate on the content of their help.
  • There is a request for a response regarding the Taylor series expansion, indicating that the participant believes there is a specific answer expected.

Areas of Agreement / Disagreement

The discussion shows a lack of consensus, with participants expressing confusion and seeking clarification without a clear resolution or agreement on the steps involved in the integral's expansion.

Contextual Notes

Limitations include unclear formatting of mathematical expressions and potential missing assumptions related to the function ⌽(u) and its behavior at uf.

arneet
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i am completely lost. there is an integral in my textbook in fermi dirac statistics whose result is written directly and am not able to understand . it is
∫⌽(u) du /exp.((u-uf)/kt) + 1 from 0 to ∞
expanded by tayor's series to give

∫⌽(u) du (from 0 to uf) +∏²/6 (kT)² [⌽'(u)] |at u=uf + 7∏⁴/360 (kT)⁴ [⌽''(u)] |at u=uf +...

where uf is such that function of u is zero for u greater than uf.
please reply as soon as possible. thanks.
 
Physics news on Phys.org
It's very hard to read the formulae. Please use LaTeX.
 
hope this could help
 

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please reply. the answer on expansion by taylor series should be
 

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