Definition.
where
Orthogonality. For 
and 
or for 
and
we have
Recurrence relation.
where
and
Normalized recurrence relation.
where
Difference equation.
where
Forward shift operator.
or equivalently
Backward shift operator.
or equivalently
where
Rodrigues-type formula.
where
Generating functions. For 
we have
Remark. If we interchange the role of x and n in the definition (1.6.1) of the dual Hahn polynomials we obtain the Hahn polynomials defined by (1.5.1).
Since
we obtain the dual orthogonality relation for the dual Hahn polynomials from the orthogonality relation (1.5.2) for the Hahn polynomials :
References. [64], [67], [69], [251], [271], [274], [297], [298], [300], [301], [323], [343], [385], [399].
