Impulse response invariant discretization of distributed order integrator

Compute a discrete-time transfer function to approximate a distributed order integrator.

irid_doi function is prepared to compute a discrete-time finite dimensional (z) transfer function to approximate a distributed order integrator int(1/s^r,r,a,b), where "s" is the Laplace transform variable. Where 'a' and 'b' are arbitrary real numbers in the range of (0.5,1), and a<b. 'p' and 'q' are integer and p>=q.
The proposed approximation keeps the impulse response "invariant".