Let $f$ be a continuous complex-valued function on the unit interval. For any complex number $z$, define $F(z)=\int _0 ^1 f(t) e^{zt} dt$.
How do I show that $F$ is entire?
Let $f$ be a continuous complex-valued function on the unit interval. For any complex number $z$, define $F(z)=\int _0 ^1 f(t) e^{zt} dt$.
How do I show that $F$ is entire?