Definition.
Orthogonality. For 
and 
or for 
and
we have
Recurrence relation.
where
and
Normalized recurrence relation.
where
Difference equation.
where
and
Forward shift operator.
or equivalently
Backward shift operator.
or equivalently
where
Rodrigues-type formula.
Generating functions. For 
we have
Remark. If we interchange the role of x and n in (1.5.1) we obtain the dual Hahn polynomials defined by (1.6.1).
Since
we obtain the dual orthogonality relation for the Hahn polynomials from the orthogonality relation (1.6.2) of the dual Hahn polynomials :
References. [13], [31], [32], [39], [43], [50], [64], [67], [69], [123], [127], [130], [136], [142], [143], [181], [183], [212], [215], [251], [271], [274], [286], [287], [290], [294], [295], [296], [298], [301], [307], [323], [336], [338], [339], [344], [366], [385], [386], [399], [402], [407].
