Lec 23 Possion formula clarification

[Kun Guo]

Attached picture is a screen shot of online notes lecture 23. I was wondering if there is an addition r in front of sin(n*theta) in (12). Also, is there missing a^(-n) in calculating An and Cn?

[Victor Ivrii]

Good catch

[Miranda Jarvis]

I don't understand, if in equation (12) we are plugging in r=a to eq(10) how is there still and r involved as a variable?

[Victor Ivrii]

I don't understand, if in equation (12) we are plugging in r=a to eq(10) how is there still and r involved as a variable?

We plug $r=a$ to recover coefficients (which do not depend on $r$). After they are recovered we plug them to the original expression for $u$ which  still contains $r$.

[Aida Razi]

I was wondering if Cn has to be sin(nθ) instead of cos(nθ)?

[Victor Ivrii]

I was wondering if Cn has to be sin(nθ) instead of cos(nθ)?

Yes, corrected.