Definition.
Orthogonality. For 
, 
and c < 0 we
have
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.
Generating functions.
Remarks. The big q-Jacobi polynomials with c = 0 and the little q-Jacobi polynomials defined by (3.12.1) are related in the following way :
Sometimes the big q-Jacobi polynomials are defined in terms of four parameters instead of three. In fact the polynomials given by the definition
are orthogonal on the interval 
with respect to the weight function
These polynomials are not really different from those defined by (3.5.1) since we have
and
References. [11], [13], [31], [67], [166], [193], [203], [206], [208], [218], [239], [242], [248], [262], [279], [282], [318], [323], [325], [326], [327], [371], [379].
Definition. The big q-Legendre polynomials are big q-Jacobi polynomials with a = b = 1 :
Orthogonality. For c < 0 we have
Recurrence relation.
where
Normalized recurrence relation.
where
q-Difference equation.
where
and
Rodrigues-type formula.
Generating functions.
