  We develop series expansions in powers of $q^{-1}$ and $q^{-1/2}$ of
solutions of the equation $\psi(z) = q$, where $\psi(z)$ is the Laplace
exponent of a hyperexponential L\'{e}vy process. As a direct consequence we
derive analytic expressions for the prices of European call and put options and
their Greeks (Theta, Delta, and Gamma) and a full asymptotic expansion of the
short-time Black-Scholes at-the-money implied volatility. Further we
demonstrate how the speed of numerical algorithms for pricing exotic options,
which are based on the Laplace transform, may be increased.
