The Laplace transforms of certain functions can be found conveniently from their Taylor series expansions.
(a) Using the Taylor series for
and assuming that the Laplace transform of this series can be computed term by term, verify that
(b) Let
Find the Taylor series for
(c) The Bessel function of the first kind of order zero,
Assuming that the following Laplace transforms can be computed term by term, verify that
And
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