q-Analogues of the sums of consecutive integers, squares, cubes, quarts and quints

Michael Schlosser
We first show how a special case of Jackson's 8 φ 7 summation immediately gives Warnaar's q-analogue of the sum of the first n cubes, as well as q-analogues of the sums of the first n integers and first n squares. Similarly, by appropriately specializing Bailey's terminating very-well-poised balanced 10 φ 9 transformation and applying the terminating very-well-poised 6 φ 5 summation, we find q-analogues for the respective sums of the first n quarts and first n quints. We also derive q-analogues
more » ... of the alternating sums of squares, cubes and quarts, respectively.