Inner products involving q-differences: the little q-Laguerre-Sobolev polynomials

22 pages, no figures.-- MSC codes: Primary 33C25; Secondary 33D45.-- Issue title: "Higher transcendental functions and their applications".MR#: MR1765938 (2001d:33018)Zbl#: Zbl 0957.33008In this paper, polynomials which are orthogonal with respect to the inner product $$\multline\langle p,r\rangle_S=\sum^\infty_{k=0}p(q^k)r(q^k) {(aq)^k(aq;q)_\infty\over(q;q)_k}\\ +\lambda\sum^\infty_{k=0} (D_qp)(q^k)(D_qr)(q^k){(aq)^k(aq;q)_\infty\over(q;q)_k},\endmultline$$ where $D_q$ is the $q$-difference operator, $\lambda\geq0,\ 0<q<1$ and $0<aq