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

[arneet]

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.

 

[vanhees71]

It's very hard to read the formulae. Please use LaTeX.

 

[arneet]

hope this could help

 

[arneet]

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