If we take the limit in the definition
(3.8.1) of the Al-Salam-Chihara polynomials we simply
obtain the continuous big q-Hermite polynomials given by (3.18.1) :
The continuous q-Hermite polynomials defined by (3.26.1)
can easily be obtained from the continuous big q-Hermite polynomials given by
(3.18.1) by taking a = 0 :