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 functions.
Remark. Since the Stieltjes and Hamburger moment problems corresponding to the Stieltjes-Wigert polynomials are indeterminate there exist many different weight functions. For instance, they are also orthogonal with respect to the weight function
References. [42], [43], [73], [122], [123], [132], [323], [387], [388], [391], [398].
