Calculating EMA/RSI by hand

I require some clarification on this as I have never been able to get the figures correct (or even close up to two to five decimal places).

When you calculate the 10-period EMA or RSI the issue I am having lies in which initial condition or seed to use. Which of these is the correct method?:

* Go back 20-periods and calculate the mean of EMA/RSI from 20 to 10 periods. Then calculate the EMA/RSI for the remaining 10-periods.

* Go back 10-periods and then calculate the mean of EMA/RSI for the first 9-periods and then the final calculation for the EMA/RSI over the last (ie, current) period.

I've tried both methods and using various data feeds the figures don't quite match up. In both scenarios the figures are close but not close enough.

EMA is a IIR filter (https://en.wikipedia.org/wiki/Infinite_impulse_response). It needs to reach steady state before its outout is valid. Try using much more than the period of the average. Like 200 periods before. Do the same for the RSI. Of course for the "by hand" part that may take some time...