I'm interested in equations for the pole locations of the Paynter filter. The publication "The Lightning Empericist" has the equations for the even order Paynter filter pole locations, and for the third order pole locations, but no equations for higher odd order filters.
The Paynter filter is an approximation to a linear phase filter. The linear phase approximation is exact at integer multiples of w0/4, where w0 is the cutoff frequency. It is not an equi-ripple filter. The values of the successive phase error ripple peaks increase with frequency.