  Inspired by the work of Bank on the hypertranscendence of $\Gamma e^h$ where
$\Gamma$ is the Euler gamma function and $h$ is an entire function, we
investigate when a meromorphic function $fe^g$ cannot satisfy any algebraic
differential equation over certain field of meromorphic functions, where $f$
and $g$ are meromorphic and entire on the complex plane, respectively. Our
results (Theorem 1 and 2) give partial solutions to Bank's Conjecture (1977) on
the hypertranscendence of $\Gamma e^h$. We also give some sufficient conditions
for hypertranscendence of meromorphic function of the form $f+g$, $f\cdot g$
and $f\circ g$ in Theorem 3 and 4.
