- Thread starter
- #1

- Jan 17, 2013

- 1,667

*Suppose that $f$ is piecewise continuous on \(\displaystyle [0,\infty) \) and of exponential order $c$ then*

is analytic in the right half-plane for \(\displaystyle \mathrm{Re}(s)>c\)

\(\displaystyle \int^\infty_0 e^{-st} f(t)\, dt \)

is analytic in the right half-plane for \(\displaystyle \mathrm{Re}(s)>c\)