Black-Scholes prices with a dividend yield

Give the Black-Scholes formulas for European call and put prices on a stock that pays a continuous dividend yield $q$.

$c=S_0e^{-qT}N(d_1)-Ke^{-rT}N(d_2)$ and $p=Ke^{-rT}N(-d_2)-S_0e^{-qT}N(-d_1)$, with $d_1=\tfrac{\ln(S_0/K)+(r-q+\frac12\sigma^2)T}{\sigma\sqrt T}$ and $d_2=d_1-\sigma\sqrt T$. The dividend yield simply replaces $S_0$ by $S_0e^{-qT}$, the value of the share without the dividends paid before expiry.