A new proof of the q -Dixon identity

Victor J. W. Guo

Czechoslovak Mathematical Journal (2018)

  • Volume: 68, Issue: 2, page 577-580
  • ISSN: 0011-4642

Abstract

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We give a new and elementary proof of Jackson’s terminating q -analogue of Dixon’s identity by using recurrences and induction.

How to cite

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Guo, Victor J. W.. "A new proof of the $q$-Dixon identity." Czechoslovak Mathematical Journal 68.2 (2018): 577-580. <http://eudml.org/doc/294372>.

@article{Guo2018,
abstract = {We give a new and elementary proof of Jackson’s terminating $q$-analogue of Dixon’s identity by using recurrences and induction.},
author = {Guo, Victor J. W.},
journal = {Czechoslovak Mathematical Journal},
keywords = {$q$-binomial coefficient; $q$-Dixon identity; recurrence},
language = {eng},
number = {2},
pages = {577-580},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A new proof of the $q$-Dixon identity},
url = {http://eudml.org/doc/294372},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Guo, Victor J. W.
TI - A new proof of the $q$-Dixon identity
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 2
SP - 577
EP - 580
AB - We give a new and elementary proof of Jackson’s terminating $q$-analogue of Dixon’s identity by using recurrences and induction.
LA - eng
KW - $q$-binomial coefficient; $q$-Dixon identity; recurrence
UR - http://eudml.org/doc/294372
ER -

References

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  1. Andrews, G. E., The Theory of Partitions, Cambridge University Press, Cambridge (1998). (1998) Zbl0996.11002MR1634067
  2. Bailey, W. N., 10.1093/qmath/os-12.1.173, Q. J. Math., Oxf. Ser. 12 (1941), 173-175. (1941) Zbl0063.00168MR0005964DOI10.1093/qmath/os-12.1.173
  3. Dixon, A. C., 10.1112/plms/s1-35.1.284, London M. S. Proc. 35 (1903), 284-289. (1903) Zbl34.0490.02MR1576998DOI10.1112/plms/s1-35.1.284
  4. Ekhad, S. B., 10.1016/0097-3165(90)90014-N, J. Comb. Theory, Ser. A 54 (1990), 141-142. (1990) Zbl0707.05007MR1051787DOI10.1016/0097-3165(90)90014-N
  5. Gessel, I., Stanton, D., 10.1016/0097-3165(85)90026-3, J. Comb. Theory Ser. A 38 (1985), 87-90. (1985) Zbl0559.05008MR0773560DOI10.1016/0097-3165(85)90026-3
  6. Guo, V. J. W., 10.1016/S0012-365X(03)00054-2, Discrete Math. 268 (2003), 309-310. (2003) Zbl1022.05006MR1983288DOI10.1016/S0012-365X(03)00054-2
  7. Guo, V. J. W., Zeng, J., 10.1016/j.disc.2005.04.006, Discrete Math. 296 (2005), 259-261. (2005) Zbl1066.05022MR2154718DOI10.1016/j.disc.2005.04.006
  8. Jackson, F. H., 0.1093/qmath/os-12.1.167, Q. J. Math., Oxford Ser. 12 (1941), 167-172. (1941) Zbl0063.03007MR0005963DOI0.1093/qmath/os-12.1.167
  9. Koepf, W., 10.1007/978-1-4471-6464-7, Universitext, Springer, London (2014). (2014) Zbl1296.33002MR3289086DOI10.1007/978-1-4471-6464-7
  10. Mikić, J., A proof of a famous identity concerning the convolution of the central binomial coefficients, J. Integer Seq. 19 (2016), Article ID 16.6.6, 10 pages. (2016) Zbl1343.05015MR3546620
  11. Mikić, J., A proof of Dixon's identity, J. Integer Seq. 19 (2016), Article ID 16.5.3, 5 pages. (2016) Zbl06600942MR3514546
  12. Petkovšek, M., Wilf, H. S., Zeilberger, D., A = B. With foreword by Donald E. Knuth, A. K. Peters, Wellesley (1996). (1996) Zbl0848.05002MR1379802
  13. Zeilberger, D., 10.1016/S0195-6698(87)80054-9, Eur. J. Comb. 8 (1987), 461-463. (1987) Zbl0643.05003MR0930183DOI10.1016/S0195-6698(87)80054-9

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