Can one show that the following integral converges on $-1<\Re s < 1$ and define holomorphic function of $s$?
$$\int_0^\infty \sin(y) y^{s-1} dy$$
I've googled for a while, but I could not find any good reference.
Can one show that the following integral converges on $-1<\Re s < 1$ and define holomorphic function of $s$?
$$\int_0^\infty \sin(y) y^{s-1} dy$$
I've googled for a while, but I could not find any good reference.