- #1

benf.stokes

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Hi,

In griffith's "Introduction to Electrodynamics" he indicates that a specific infinite series has a truncated form (the series and truncated form are given below)

And he says the reader can try to show that it indeed has that form.

[itex] \frac{4V_0}{\pi}\sum_{n=1,3,5,7,...}^{\infty}\frac{1}{n}e^{-n\pi x/a}sin(n\pi y/a)=\frac{2V_0}{\pi}arctg(\frac{sin(\pi y/a)}{sinh(\pi x/a)}) [/itex]

However I can't figure out how to get that result. Can anybody help me figure it out, without starting from the truncated form?

In griffith's "Introduction to Electrodynamics" he indicates that a specific infinite series has a truncated form (the series and truncated form are given below)

And he says the reader can try to show that it indeed has that form.

[itex] \frac{4V_0}{\pi}\sum_{n=1,3,5,7,...}^{\infty}\frac{1}{n}e^{-n\pi x/a}sin(n\pi y/a)=\frac{2V_0}{\pi}arctg(\frac{sin(\pi y/a)}{sinh(\pi x/a)}) [/itex]

However I can't figure out how to get that result. Can anybody help me figure it out, without starting from the truncated form?

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