# fourier series for exponentialsWatch

#1
hi, there are the fourier series i obtained for e^x, sinhx and coshx, please can you verify if they are correct.

(QUESTION A)

fourier series for e^x:

fourier series for sinh(x):

fourier series for cosh(x) = 0..

are these correct?

(QUESTION B)
i need some help working out the An and Bn of the fourier series for e^x:

for example for e^x, how can you show:

my working doesnt seem to arrive . here is my working:

to integrate

u= e^x, du = e^x ................ dv= cos(nx), v = (sin(nx)/n)
so =

but the 2nd part (i.e , is a never ending process since the e^x will never vanish. as a result i am not able to go on further with this problem. so could you please explain how we arrive at the final answer being:
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11 years ago
#2

For the next bit, you're on the right lines. By repeated integration by parts (here I'm integrating e^x and differentiating cos(nx)) :

Solving for and dividing by gives:

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11 years ago
#3
Funny how in the last few hours has come up twice in two unrelated posts!
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#4
thanks a lot
i've worked it out properly now and i get the same answer as you except for one part:

is there a typo in this series: i.e. look at the sum formula...
you have done

where did the n(-1)^n+1 come from... is it not meant to be just (-1)^n+1 without the extra "n" at the front..

and most important question:
Can the fourier series for sinhx, coshx, and e^x be shown in a more simpler form? or is this the simplest form?
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11 years ago
#5

Solving for and dividing by gives:

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