Four tensor products of evaluation modules of the quantum affine algebra \documentclass[12pt]{minimal}\begin{document}$U^{\prime }_q\bigl (\widehat{sl}(2)\bigr )$\end{document}Uq′sl̂(2) obtained from the negative and positive series, the complementary and the strange series representations are investigated. Linear operators R(z) satisfying the intertwining property on finite linear combinations of the canonical basis elements of the tensor products are described in terms of two sets of infinite sums \documentclass[12pt]{minimal}\begin{document}$\lbrace \tau ^{(r,t)}\rbrace _{r,t\in \mathbb {Z}_{\ge 0}}$\end{document}{τ(r,t)}r,t∈Z≥0 and \documentclass[12pt]{minimal}\begin{document}$\lbrace \check{\tau }^{(r,t)}\rbrace _{r,t\in \mathbb {Z}_{\ge 0}}$\end{document}{τ̌(r,t)}r,t∈Z≥0 involving big q2-Jacobi functions or related nonterminating basic hypergeometric series. Inhomogeneous recurrence relations can be derived for both sets. Evaluations of the simplest sums provide the corresponding initial conditions. For the first set of sums the relations entail a big q2-Jacobi function transform pair. An integral decomposition is obtained for the sum τ(r, t). A partial description of the relation between the decompositions of the tensor products with respect to \documentclass[12pt]{minimal}\begin{document}$U_q\bigl (sl(2)\bigr )$\end{document}Uqsl(2) or with respect to its complement in \documentclass[12pt]{minimal}\begin{document}$U^{\prime }_q\bigl (\widehat{sl}(2)\bigr )$\end{document}Uq′sl̂(2) can be formulated in terms of Askey-Wilson function transforms. For a particular combination of two tensor products, the occurrence of proper \documentclass[12pt]{minimal}\begin{document}$U^{\prime }_q\bigl (\widehat{sl}(2)\bigr )$\end{document}Uq′sl̂(2)-submodules is discussed.