So, I have the series of [itex]g(x) = e^{(x-1)^{2}} = 1 + (x-1)^{2} + \frac{(x-1)^{4}}{2} + \frac{(x-1)^{6}}{6} + ... + \frac{(x-1)^{2n}}{n!} [/itex](adsbygoogle = window.adsbygoogle || []).push({});

and I am asked to find the series of [itex]f(x) = \frac{e^{(x-1)^{2}}-1}{(x-1)^{2}}[/itex] for x [itex]\neq[/itex] 1 and f(1) = 1. The Taylor series is centered about x = 1

I am told that there is an easy way to do this, but I don't see it.

any help would be appreciated, thanks

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# Shortcut to taylor series of f, given taylor series of g

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