Definition.
Orthogonality.
Recurrence relation.
where
Normalized recurrence relation.
where
q-Difference equation.
where
and
Forward shift operator.
or equivalently
Backward shift operator.
or equivalently
where
Rodrigues-type formula.
where
Generating functions.
Remarks. The q-Meixner polynomials defined by (3.13.1) and the little q-Jacobi polynomials given by (3.12.1) are related in the following way :
The q-Meixner polynomials and the quantum q-Krawtchouk polynomials defined by (3.14.1) are related in the following way :
References. [13], [26], [27], [28], [67], [104], [193], [208], [323].
