The multiple sum formulas for 12j coefficients of SU(2) and uq(2)

The expressions for 12j coefficients of the both kinds (without and with braiding) of the SU(2) group and the quantum algebra uq(2) are considered. Using Dougall's summation formula of the very well-poised hypergeometric 5F4(1) series and its q-generalization, several fourfold sum formulas [with each sum related to the balanced 5F4(1) or 5φ4 series] for the q-12j coefficients of the second kind (without braiding) are derived. Applying q-generalizations of rearrangement formulas of the very well-poised hypergeometric 6F5(-1) series [which correspond to a new expression for the Clebsch-Gordan coefficients of SU(2) and uq(2)], the new expressions with five sums [of the 4F3(1) and 3F2(1) or 4φ3 and 3φ2 type] are derived for the q-12j coefficients of the first kind (with braiding) instead of the usual expansions in terms of q-6j coefficients. Stretched and doubly stretched q-12j coefficients [as triple, double, or single sums, related to composed or separate hypergeometric 4F3(1) and 5F4(1) or 4φ3 and 5φ4 series and, particularly, to q-9j or q-6j coefficients] are considered