Geodesic
A new proof of the $q$-Dixon identity
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 2, pp. 577-580 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
We give a new and elementary proof of Jackson's terminating $q$-analogue of Dixon's identity by using recurrences and induction.
DOI : 10.21136/CMJ.2018.0052-17
Classification : 05A30
Keywords: $q$-binomial coefficient; $q$-Dixon identity; recurrence 
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     title = {A new proof of the $q${-Dixon} identity},
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Guo, Victor J. W. A new proof of the $q$-Dixon identity. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 2, pp. 577-580. doi: 10.21136/CMJ.2018.0052-17

[1] Andrews, G. E.: The Theory of Partitions. Cambridge University Press, Cambridge (1998). | MR | JFM

[2] Bailey, W. N.: A note on certain $q$-identities. Q. J. Math., Oxf. Ser. 12 (1941), 173-175. | DOI | MR | JFM

[3] Dixon, A. C.: Summation of a certain series. London M. S. Proc. 35 (1903), 284-289. | DOI | MR | JFM

[4] Ekhad, S. B.: A very short proof of Dixon's theorem. J. Comb. Theory, Ser. A 54 (1990), 141-142. | DOI | MR | JFM

[5] Gessel, I., Stanton, D.: Short proofs of Saalschütz and Dixon's theorems. J. Comb. Theory Ser. A 38 (1985), 87-90. | DOI | MR | JFM

[6] Guo, V. J. W.: A simple proof of Dixon's identity. Discrete Math. 268 (2003), 309-310. | DOI | MR | JFM

[7] Guo, V. J. W., Zeng, J.: A short proof of the q-Dixon identity. Discrete Math. 296 (2005), 259-261. | DOI | MR | JFM

[8] Jackson, F. H.: Certain $q$-identities. Q. J. Math., Oxford Ser. 12 (1941), 167-172. | DOI | MR | JFM

[9] Koepf, W.: Hypergeometric Summation---An Algorithmic Approach to Summation and Special Function Identities. Universitext, Springer, London (2014). | DOI | MR | JFM

[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. | MR | JFM

[11] Mikić, J.: A proof of Dixon's identity. J. Integer Seq. 19 (2016), Article ID 16.5.3, 5 pages. | MR | JFM

[12] Petkovšek, M., Wilf, H. S., Zeilberger, D.: A = B. With foreword by Donald E. Knuth. A. K. Peters, Wellesley (1996). | MR | JFM

[13] Zeilberger, D.: A $q$-Foata proof of the $q$-Saalschütz identity. Eur. J. Comb. 8 (1987), 461-463. | DOI | MR | JFM

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