These are very cool springs. They make great electrical connectors in medical devices, and electronics.
Of the many patents, Peter J Balsells is one of the main creators.

In one patent, the springs are not just a simple helix of steel which is pushed into a groove, circular or otherwise.
During the winding, different angles are created in the steel.
Contrary to this, the thesis formula appears to be symetrical in the z axis...

For a script, I would make the assumption that the spring runs along a straight line, not a circle, and then use flow. (?)

One iteration would make one coil, of 1/w offset.
To script along a circle, I think would require another equation, which would rotate each coil around a polygon, (or circle).
The polygon would have the same number of sides as number of coils.
Or the circle would have to have the correct circumference to accomodate an integer number of coils...

Michaels method looks excellent for viewing the circular canted coil.

A script would be fairly easy, I think.