The Jacobi polynomials defined by (1.8.1) simply follow from the little q-Jacobi polynomials defined by (3.12.1) in the following way :
If we take , for arbitrary real and in the definition (3.12.1) of the little q-Jacobi polynomials and then take the limit we obtain the Laguerre polynomials given by (1.11.1) :
If we take the limit in the definition (3.12.12) of the little q-Legendre polynomials we simply find the Legendre (or spherical) polynomials given by (1.8.57) :