Question

Check my answer! Complex form of Fourier series.

Complex form of Fourier Series for the functions f(x)=e^(ax ) in (0,a)

i got (in comments)

Answer 1

\[\Large e^{(ax)} = 2 (e^{a^2}-1) \sum \limits_{-\infty}^{\infty} \dfrac{1}{(a^2-2\pi i n)(e^{inx})}\]

Answer 2

just wanna make sure about those bounds, something fishy

Answer 3

nvm its fine

Answer 4

why is it 2/a and not 1/a

Answer 5

hmm...should be 1/a

Answer 6

new answer

\(\Large e^{(ax)} = (e^{a^2}-1) \sum \limits_{-\infty}^{\infty} \dfrac{1}{(a^2-2\pi i n)(e^{inx})}\)

Answer 7

anymore errors ?

Answer 8

looks good

Answer 9

i wonder if there is a way to rearrange the right side into a taylor series form of e^ax to verify this must be true

Answer 10

would be glad if i get one more confirmation ...just to be double sure...

Answer 11

I've been a bit distracted, but after looking over it, it seems to be correct to me as well.

Answer 12

thank you :D