Definition.
Orthogonality.
Recurrence relation.
Normalized recurrence relation.
where
q-Difference equation.
Forward shift operator.
or equivalently
Backward shift operator.
or equivalently
where
Rodrigues-type formula.
Generating function.
Remark. The Al-Salam-Carlitz I polynomials are related to the Al-Salam-Carlitz II polynomials defined by (3.25.1) in the following way :
References. [13], [17], [19], [60], [67], [121], [123], [132], [193], [216], [233], [252], [410].
