Sharp Deficiency Bounds for Meromorphic Functions in the Unit Disc

In 1986, Shea and Sons obtained the following bound for a meromorphic function $f$ of finite order $ρ$ in the unit disc, under the hypothesis $0<λ(f)\leq+\infty$, and for every positive integer $n$: \[ \sum_{a\ne\infty}δ(a,f) \leq δ(0,f^{(n)})\bigl(1+n k(f)\bigr) +\frac{2n(ρ+1)}{λ(f)}. \] Unde