Is the following integral transformation of $f$ known? (for suitable f$f$ and $s\in\mathbb{C}$):
$\int_1^\infty f(t) \frac{e^{-ts}}{1-e^{-ts}}dt$
It? $$ \int_1^\infty f(t) \frac{e^{-ts}}{1-e^{-ts}}dt $$ It resembles somewhat the Laplace transformation.
What about properties, references ...
Thanks in advance!…?