In this section, they derive the Sommerfeld formula.(adsbygoogle = window.adsbygoogle || []).push({});

In the first step it seems like they have expanded ##\frac{1}{(1+e^x))^2}##. I'm not sure why does the series taylor expand as ##e^{-nx}##?

Also how did they get from the 2nd to the 3rd step?

Simply by comparing terms we see they are different:

For 2nd step we get terms of ##x^se^x(-1 + 2e^{-x} - 3e^{-2x} + ...)##.

For 3rd step we get terms of ##e^{-x} - 2e^{-2x} + 3e^{-3x} - ....##

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Expansion of [1+exp(x)]^-2

Loading...

Similar Threads for Expansion 1+exp |
---|

I Taylor expansion of f(x+a) |

I Asymptotic expansion integral initial step |

I Taylor expansions, limits and domains |

I Taylor expansion of 1/distance |

I Small angle expansions for sin, cos, and tan |

**Physics Forums | Science Articles, Homework Help, Discussion**