A note on a result of Singh and Kulkarni (Q1567223)

We prove that if \(f\) is a transcendental meromorphic function of finite order and \(\sum_{a\neq \infty}\delta (a,f)+\delta (\infty,f)=2\), then \[ K(f^{(k)}) ={2k(1-\delta (\infty,f))\over 1+k-k\delta (\infty,f)}, \] where \[ K(f^{(k)})= \lim_{r\to \infty}{N (r,1/f^{(k)}) +N(r,f^{(k)}) \over T(r,f^{(k)})}. \] The result improves a result by Singh and Kulkarni.