See also Suslov (2003).
See §5.18.
These were introduced in Carlitz (1954a, 1958). The βn(x,q) are, in fact, rational functions of q, and not necessarily polynomials. The Am,s(q) are always polynomials in q, and the am,s(q) are polynomials in q for 0≤s≤m.
See §§17.8 and 20.5.
See §§18.27–18.29.