Vh = the desired heater voltage
Ih = the desired heater current.
To render the formula more user friendly, we rewrite it as such:
C = 159155 ,
Fwall x \/¯(Vwall² - Vh²)
now C is in microFarads. For example, four EL34s heaters in series requires 25.6 volts and 1.5 amps of current. Pluging these values into the equation yields:
33.9 µF = 159155 ,
60 x \/¯(120² - 25.6²)
which is a fairly large capacitor value that could be made up of two 100 volt 68 µF electrolytic capacitors in series or one 34 µF 200 volt Mylar capacitor. What wattage rating should the capacitor have? None. The capacitor does not dissipate any heat. Resistors dissipate heat, perfect reactive devices do not. The operative word in the previous sentence was "perfect." Inductors made of wire have a DCR (DC resistance) and capacitors made of anything other than vacuum have ESR (equivalent series resistance). So some heat will be dissipated by the capacitor, which is an argument against the use of an electrolytic capacitor.
Current regulation for Heaters
Using a voltage regulator to maintain a constant voltage for the heaters is obvious. But using a voltage regulator as a current source to maintain a constant current flow into the heaters is less so.
One three pin adjustable voltage regulator and one resistor are all that is needed to make a current source, a high current one at that. The desired current is set by the value of the resistor, which is found by dividing the base voltage (1.25 volts usually) by the desired current. For example, if we want 900 mA, we use a 1.39 resistor, as 1.39 = 1.25 / 0.9 . This resistor will dissipate over one watt of heat in this example and must be rated for at least twice that value.
The advantage to the current source approach over the fix voltage one is that the current source intrinsically limits the current inrush to the cold heater to no more than its fixed current setting. This will greatly limit heater failures. A further advantage is that the current source based power supply is much less prone to odd output oscillations than the voltage regulator based one. I believe this is so because the output of the regulator does directly attach to a capacitor in the current source version, as the current setting resistor buffers it output. The falling feedback ratio with higher frequencies within the regulator creates an inductive quality in the regulator that can be provoked into oscillation with the capacitance presented by the output capacitor.
(The ninth 1989 issue of Electronic Design carried an excellent article by Errol Dietz, titled "Reduce Noise In Voltage Regulators." The author explained nicely why certain capacitor values provoked certain frequency oscillations and why an cheap electrolytic worked better than a expensive polypropylene capacitor at preventing oscillations.)
The limitation to the current source version is that it should be used only with single heaters or a series of heaters, but not a group of parallel heaters. If two 450 mA heater elements are used in parallel with a current source and one is removed, then the other will see twice the current it should.
Even if multiple current sources are needed in an amplifier, the simplicity of the current source version makes the current source version very attractive. And the relatively low current limitation of most IC voltage regulators also makes multiple current sources a safer approach.