I'll try to explain the equation, and its shortcomings:
The capacitor charges through the rectifier until the sine wave peak passes. Then the diode becomes reverse-biased, and ceases to conduct. The capacitor then starts to discharge (assuming a constant current load) at the rate of v=I*t/C. At some point during the discharge, the voltage on the anode of the other diode in the rectifier becomes more positive than the load voltage, causing the cap to begin to charge again. If the discharge had proceeded for a complete half cycle (that's the "1/2F" term in the equation), the equation would be exact. However, as I said, the discharge ramp is terminated when the rectifier gets forward biased. As the ripple gets larger, this happens earlier in the half-cycle, causing the calculated error to be greater as the ripple increases.
Did that make sense?