5.25 Al-Salam-Carlitz II --> Charlier / Hermite

Al-Salam-Carlitz II --> Charlier

If we set and in the definition (3.25.1) of the Al-Salam-Carlitz II polynomials and taking the limit we find

Al-Salam-Carlitz II --> Hermite

If we set and in the definition (3.25.1) of the Al-Salam-Carlitz II polynomials, divide by , and let q tend to one we obtain the Hermite polynomials given by (1.13.1) with shifted argument. In fact we have