Michael J. Schlosser
q-Analogues of the sums of consecutive integers, squares,
cubes, quarts and quints
We first show how a special case of Jackson's
8φ7 summation immediately gives
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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