I have the ordinary Black-Scholes formula that reads:
$C = S(0) \Phi (d_1) - K e^{-r(T-t_0)}\Phi(d_2)$
Given the following strike price:
$K=e^{r(T-t_0)}S(0)$
I have reduced the above formula as follows:
$C=S(0)\Big[\Phi(d_1)-\Phi(d_2)\Big]$
where $d_1 = \sqrt{T-t_0} \Big(\frac{2r-1/2 \sigma^{2}}{\sigma}\Big)$ and $d_2 = \sqrt{T-t_0} \Big(\frac{2r+1/2 \sigma^{2}}{\sigma}\Big)$
Is a further reduction in terms of the cumulative distribution function operation possible?
Thanks