- Thread starter
- #1
- Jan 17, 2013
- 1,667
Prove the following
Suppose that $f$ is piecewise continuous on \(\displaystyle [0,\infty) \) and of exponential order $c$ then
is analytic in the right half-plane for \(\displaystyle \mathrm{Re}(s)>c\)
Suppose that $f$ is piecewise continuous on \(\displaystyle [0,\infty) \) and of exponential order $c$ then
\(\displaystyle \int^\infty_0 e^{-st} f(t)\, dt \)
is analytic in the right half-plane for \(\displaystyle \mathrm{Re}(s)>c\)