Taylor and Laplace

[where_was_i]

f(t)=e-t2. Find a taylor series for f(t) about x=0. Assuming it can be done term by term, find an expansion for Laplace{f}(s). If possible, sum the series. My series in the s-domain is 0!/(0!s)-2!/(1!s3)+4!/(2!s5)-6!/(3!s7I tried integrating and differentiating term by term to find a sum for it, but no luck. Is that series equal to a function

Comments

[joshua_green]

That looks good to me.
Of course it's a function.  I guess you want to know if it can be expressed in elementary form.  It should be some sort of error function, so no.

[where_was_i]

That's indeed what I was asking. My eloquence was ebbing at the time I asked, though. Thanks much.