How were the inductor values chosen for this power supply filter?

The circuit appears on this page of the online textbook.

Previously on the same page, we were shown how to calculate desired L and C values when a resistor is placed in series with the voltage source. However in this circuit, there is no resistor in series.

 

Assuming you put a 1K resistor in series with the source, the math* shown previously on the page gives values of L1 and L2 as 9500H each...

*filter_impedance = sqrt( L / C )

 

Hello,

Normally you will have some kind of impedance in series with the source. If you want to match input and output impedances, then you could calculate the input impedance and the output impedance, then choose L1 and L2 based on those equations probably using simultaneous equations.

The input Z is the impedance looking into the input of the first inductor with the load connected but no source.
The output Z is the impedance looking into the right end of the second inductor with the source connected but no load.

Filter requirements for filters like this usually have some sort of ripple specification with it so you know how much filtering you need.