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{\(q\)}-analogues of the sums of consecutive integers, squares, cubes, quarts and quints
The electronic journal of combinatorics, Tome 11 (2004) no. 1
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We first show how a special case of Jackson's ${}_8\phi_7$ 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 ${}_{10}\phi_9$ transformation and applying the terminating very-well-poised ${}_6\phi_5$ 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.
DOI : 10.37236/1824
Classification : 33D15, 05A15 
@article{10_37236_1824,
     author = {Michael Schlosser},
     title = {{\(q\)}-analogues of the sums of consecutive integers, squares, cubes, quarts and quints},
     journal = {The electronic journal of combinatorics},
     year = {2004},
     volume = {11},
     number = {1},
     doi = {10.37236/1824},
     zbl = {1064.33014},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1824/}
}
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Michael Schlosser. {\(q\)}-analogues of the sums of consecutive integers, squares, cubes, quarts and quints. The electronic journal of combinatorics, Tome 11 (2004) no. 1. doi: 10.37236/1824

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