Definition.
Orthogonality.
where
with
Recurrence relation.
Normalized recurrence relation.
where
q-Difference equation.
where
Forward shift operator.
or equivalently
Backward shift operator.
or equivalently
Rodrigues-type formula.
Generating functions.
Remark. The continuous q-Hermite polynomials can also be written as :
References. [7], [13], [14], [24], [31], [43], [44], [53], [54], [58], [64], [65], [66], [67], [73], [83], [93], [98], [101], [165], [189], [193], [219], [229], [238], [240], [323], [363], [364], [365], [378].
