Definition.
Orthogonality.
Recurrence relation.
where
Normalized recurrence relation.
where
q-Difference equation.
where
Forward shift operator.
or equivalently
Backward shift operator.
or equivalently
where
Rodrigues-type formula.
Generating function.
Remarks. The little q-Jacobi polynomials defined by (3.12.1) and the big q-Jacobi polynomials given by (3.5.1) are related in the following way :
The little q-Jacobi polynomials and the q-Meixner polynomials defined by (3.13.1) are related in the following way :
References. [11], [13], [22], [23], [30], [31], [43], [67], [167], [168], [169], [190], [193], [203], [208], [218], [231], [242], [259], [263], [277], [279], [280], [282], [313], [318], [323], [346], [377], [379], [382].
Definition. The little q-Legendre polynomials are little q-Jacobi polynomials with a = b = 1 :
Orthogonality.
Recurrence relation.
where
Normalized recurrence relation.
where
q-Difference equation.
where
and
Rodrigues-type formula.
Generating function.
References. [279], [280], [351], [392].
