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 #1
Please refer to the attachment.
For part a)
so far I have:
$e^x = 1 + \frac{x}{1!} + ...+ \frac{x^n}{n!}$
So
$S^\frac{1}{2}e^\frac{1}{S} = S^\frac{1}{2}(1 \frac{1}{S} + \frac{1}{2!S^2}  \frac{1}{3!S^3} + \frac{1}{4!S^4} + ...  ...)$
I don't think my $S^\frac{1}{2}$ on the outside is correct though.
I don't know why it says 'take the inverse transform term by term', since this is a never ending series.
Little lost for part 2. They haven't covered it in lectures yet, I briefly recall this being related to the cauchy integral formula... or something similar we did earlier.
Any help is appreciated,
Thanks!
For part a)
so far I have:
$e^x = 1 + \frac{x}{1!} + ...+ \frac{x^n}{n!}$
So
$S^\frac{1}{2}e^\frac{1}{S} = S^\frac{1}{2}(1 \frac{1}{S} + \frac{1}{2!S^2}  \frac{1}{3!S^3} + \frac{1}{4!S^4} + ...  ...)$
I don't think my $S^\frac{1}{2}$ on the outside is correct though.
I don't know why it says 'take the inverse transform term by term', since this is a never ending series.
Little lost for part 2. They haven't covered it in lectures yet, I briefly recall this being related to the cauchy integral formula... or something similar we did earlier.
Any help is appreciated,
Thanks!
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