Express-f-x-x-t-e-x-as-a-series-

Question Number 9804 by FilupSmith last updated on 05/Jan/17

Express f (x) = x^{t} e^{x} as a series

Commented by FilupSmith last updated on 07/Jan/17

x^{t} = e^{t \ln (x)}

= \underset{n = 0}{\sum^{\infty}} \frac{t^{n} \ln^{n} (x)}{n!}

∴ x^{t} e^{x} = \underset{n = 0}{\sum^{\infty}} \frac{t^{n} e^{x} \ln^{n} (x)}{n!}