{\(q\)}-analogues of the sums of consecutive integers, squares, cubes, quarts and quints
Summary: We first show how a special case of Jackson's \(_8 \varphi_7\) 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 \(_{10} \varphi_9\) transformation and applying the terminating very-well-poised \(_6\varphi_5\) 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.
scientific article; zbMATH DE number 2161295