The first two questions follow directly from applying the residue theorem to the Mellin transforms.

In the third one you just have to consider the contribution from the residue at $s=1$.

The paper is research-level, but these kind of questions fit better at math.stackexchange.

The first two questions follow directly from applying the residue theorem to the Mellin transforms.

In the third one you just have to consider the contribution from the residue at $s=1$.

The paper is research-level, but these kind of questions fit better at math.stackexchange.

The first two questions follow directly from applying the residue theorem to the Mellin transforms.

In the third one you just have to consider the contribution from the residue at $s=1$.

The paper is research-level, but these kind of question fit better at math.stackexchange.

The first two questions follow directly from applying the residue theorem to the Mellin transforms.

In the third one you just have to consider the contribution from the residue at $s=1$.

The paper is research-level, but these kind of questions fit better at math.stackexchange.