It is more a matter of testing for optimal zener current rather then using a formula.
There are two different voltage regulating effects that occur in a "zener" diode. Below about 4.7V, the zener effect dominates and it has a temp coefficient of about -3mV/C. About 8V, avalanche breakdown dominates and this has a positive temp coefficient - the size of the coefficient increases with breakdown voltage.
Somewhere in the 5.2V - 6.8V range, you have devices that can be set to near 0mv/C coefficient by finding the optimal current. So for a particular family of zeners, get 5.2V, 5.6V, 6.2V, 6.8V values and attach to a variable current source (ie power supply + resistor + multimeter). Vary the current, and using your finger to raise the temperature initially, look for a current with a zero coefficient. You can even try different base-emitter transistor junctions if you want to instead of the zener diode. The compensation is not perfect. If you pick a zero TC point of say 25C, you can get fairly good regulation over maybe +/-5 degC.
Now zero TC does not mean stability. Ordinary zeners will drift over time due to issues like surface defects and contamination. Zeners are also noise sources, and different zeners will have different amounts of noise. Some of this noise is very low frequency - such as 0.1Hz or 0.01Hz, so you cannot just eliminate it with a big capacitor.
Richard.