Definition.
Orthogonality. If 
and non-real parameters
occur in conjugate pairs, then
where
If a < 0 and a+b, a+c, a+d are positive or a pair of complex conjugates occur with positive real parts, then
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.
Remark. If we set
and
in
defined by (1.1.1) and take
we obtain the Racah polynomials defined by (1.2.1).
References. [43], [63], [64], [67], [225], [226], [273], [274], [312], [317], [391], [399], [400].
