Interpolating the Derivatives of the Gamma Function

We consider a function $G(\lambda ,z)$, entire in $\lambda$, which interpolates the derivatives of the Gamma function in the sense that $G(m, z) = \Gamma^{(m)}(z)$foranyinteger$m \geq 0$andwecalculatetheasymptoticsof$G(\lambda, z)$as$\lambda \to +\infty$.