Yes it is valid for any function

I am not sure what you are trying to say. The RMS value does not depend on time values, within reason. If you have a signal which is on for 3 days and then off for 3 days, then you can consider it as a DC signal depending on the corresponding processes in your system.

For example: You try to determine what connector you can choose, based on the RMS value of the current that has to go through one pin. If you have a PWM signal of say, 100 kHz, then yes, you can use the RMS value. But if you have a signal with a period of 10 seconds, then you have to look at the maximum value of the current over 10 seconds. That spec becomes now DC, not AC.

The period of 1 sec has an on time that’s much longer than a period of 1usec, but then it also has a longer off time, so it cancels out.

I need to find the DC equivalent of a current pulse and based on some articles I read, it would be the RMS value. However, looking at the equation of RMS for a square wave, for a particular duty cylce say 50%, no matter what my period would be, the RMS will always be the same. For example, if I have a pulse of 100A, the RMS would be 70.7A whether the period is 1 sec. or 1 us. This doesn’t feel right because I would expect the DC equivalent for a 1sec period to be greater than a 1us period. What do you think? Is the average of the current pulse more appropriate? Thanks in advance for any input you can provide.

Yes, you do. The RMS current can be used in the formula regardless if the waveform is sine or square wave.

Because, physically, they both produce the same amount of power.

Why? Therefore, this is a coincidence? Or it is about first harmonic of a half square wave is equal to a sinwave?

I am going to assume that you set your multimeter on RMS measurement. It measures correctly when the duty-cycle is 50% and then errors out as the duty-cycle goes to extremes. Most likely this is due to multimeter’s insufficient bandwidth. Comments invited.