Contiguous relations, basic hypergeometric functions, and orthogonal polynomials. II. Associated big q-Jacobi polynomials

Abstract

Explicit solutions to the recurrence relation for the associated big q-Jacobi polynomials are obtained using 3 φ 2 contiguous relations. A new continued fraction is derived with the help of the minimal solution. The orthogonality for polynomial solutions in some special cases is discussed. Two exceptional cases yield the basic analogues of Entry 25 and Entry 33 in Chapter 12 of Ramanujan's second notebook. Connections of the general case with other associated cases are indicated.