e-mail: coskun@math.tamu.edu

**The analogue of Jackson's summation theorem for the
affine root system $B_1^{\vee}$ and its applications**

**Abstract**

The analogue of the Jackson's sum of a terminating very well-poised balanced $_8\phi_7$ series for the affine root system $B_1^\vee$ is proved. A couple of very interesting applications of this result is presented.