Confusion regarding a library of Digital Signal Controller
The function you are refering to only implements an order-1 filter. There is another function for order-2 filter.

If you want to implement an order-3 filter, you will have to split it in an order-1 filter and an order-2 filter. There are many ways to do it, but cascading the filters, as we would do in the analog world, is a good solution, albeit not optimal IIRC.

As to your original question, since the function refers to an order-1 IIR filter, an order-1 Elliptic or Butterworth, will have the same coefficients if you design them with the same cut-off frequency.

However, starting with order 2 or more, the coefficients will not be the same.