Michael J. Schlosser

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

(12 pages)

Abstract. We first show how a special case of Jackson's ₈Φ₇ 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 ₁₀Φ₉ transformation and applying the terminating very-well-poised ₆Φ₅ summation, we find q-analogues for the respective sums of the first n quarts and first n quints. We also derive q-analogues of the alternating sums of squares, cubes and quarts, respectively.

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