what is the Mellin trasnform of the Digamma function ??
from Ramanujan master theorem http://mathworld.wolfram.com/RamanujansMasterTheorem.html
y believe it should be equal to
$$ \int_{0}^{\infty}dx\psi(x+1)x^{s-1}=\frac{-\pi}{\sin (\pi s)}\zeta(1-s) $$
i have used the expansion $$ \Psi(x+1)= -\sum_{n=0}^{\infty}(-z)^{n}\zeta (k+1)$$
wit the 'regularization' $ \zeta (1)= \gamma $ Euler mascheroni constant.