(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

This isn't really a homework question, but something I've been wanting to know out of curiosity in David Griffiths' Introduction to Electrodynamics.

On pages 131 and 132, there is a Fourier series,

[tex]V(x,y) = \frac{4V_0}{\pi}\sum_{n=1,3,5...}\frac{1}{n}e^{\frac{-n \pi x}{a}}\sin{\frac{n \pi y}{a}}[/tex]

The author then says that the series can be rewritten as

[tex]V(x,y) = \frac{2V_0}{\pi} \arctan{\frac{\sin{\frac{\pi y}{a}}}{\sinh{\frac{\pi x}{a}}}}[/tex]

The author says "the infinite series ... can be summed explicitly (try your hand at it, if you like) ..." so I got curious and decided to take a shot at it.

I have been trying to figure out how to get this result all day, but after a few sheets of paper, I am still lost... Any help would be much appreciated.

P.S. I have not taken a course on complex analysis.

2. Relevant equations

[tex]\sin{u} = \frac{e^{iu}-e^{-iu}}{2i}[/tex]

[tex]\sinh{u} = \frac{e^{u}-e^{-u}}{2}[/tex]

[tex]\arctan{u} = \frac{i}{2}\ln{\frac{1-iu}{1+iu}}[/tex]

[tex]\arctan{u} = \sum_{n=0}^{\inf} \frac{(-1)^n}{2n+1} u^{2n+1}[/tex]

3. The attempt at a solution

**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!

# Homework Help: Fourier series summation in David Griffiths' textbook

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