Inversion techniques and combinatorial identities. Jackson’s q-analogue of the Dougall-Dixon theorem and the dual formulae
Compositio Mathematica, Tome 95 (1995) no. 1, pp. 43-68. 
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     author = {Chu, Wenchang},
     title = {Inversion techniques and combinatorial identities. {Jackson{\textquoteright}s} $q$-analogue of the {Dougall-Dixon} theorem and the dual formulae},
     journal = {Compositio Mathematica},
     pages = {43--68},
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     url = {http://archive.numdam.org/item/CM_1995__95_1_43_0/}
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Chu, Wenchang. Inversion techniques and combinatorial identities. Jackson’s $q$-analogue of the Dougall-Dixon theorem and the dual formulae. Compositio Mathematica, Tome 95 (1995) no. 1, pp. 43-68. http://archive.numdam.org/item/CM_1995__95_1_43_0/

1 G.E. Andrews: Connection coefficient problems and partitions, Proc. Symp. Pure Math. 34 (1979) 1-24. | MR | Zbl

2 R. Askey: Variants of Clausen's formula for the square of a special 2F 1, in Number Theory and Related Topics, Tata Institute of Fundamental Research, Bombay, 1988. | MR | Zbl

3 W.N. Bailey: Generalized Hypergeometric Series, Cambridge University Press, London, 1935. | JFM | Zbl

4 D.M. Bressoud: The Bailey lattice: an introduction, 57-67 in Ramanujan Revisited (G. E. Andrews et al. eds.), Academic Press, New York, 1988. | MR | Zbl

5 L. Carlitz: Some inverse relations, Duke Math. J. 40 (1973) 893-901. | MR | Zbl

6 W.C. Chu: A class of bivariate reciprocal formulas and applications to combinatorial identities (Chinese, English summary), Appl. Math. 1(3) (1988) 63-66. | MR | Zbl

7 W.C. Chu: Inversion techniques and combinatorial identities: Strange evaluations of basic hypergeometric series, Compositio Math. 9 (1994), 121-144. | Numdam | MR | Zbl

8 W.C. Chu: Symmetry on q-Pfaff-Saalschutz-Sheppard series, Rivista di Mat. N11 (1992), 73-79. | MR | Zbl

9 W.C. Chu and L.C. Hsu: Some new applications of Gould-Hsu inversions, J. Combin., Informat., Systems Sci. 14(1) (1990) 1-4. | MR | Zbl

10 S.B. Ekhad: A short proof of a terminating "strange" hypergeometric summation formula of Gasper and Rahman, Preprint, 1990.

11 H. Exton: Q-Hypergeometric Series and Applications, Ellis Horwood Limited, England, 1983. | MR | Zbl

12 G. Gasper: Summation, transformation and expansion formulas for bibasic series, Trans. Amer. Math. Soc. 312(1) (1989) 257-277. | MR | Zbl

13 G. Gasper and M. Rahman: An indefinite bibasic summation formula and some quadratic, cubic and quartic summations and transformation formulas, Can. Math. J. 17(1) (1990) 1-27. | MR | Zbl

14 G. Gasper and M. Rahman: Basic hypergeometries series, vol. 35, in Encyclopedia of Mathematics and Its Application (ed. G. C. Rota); Cambridge University Press, Cambridge, 1990. | MR | Zbl

15 Ira Gessel and D. Stanton: Strange evaluations of hypergeometric series, SIAM J. Math. Anal. 13 (1982) 295-308. | MR | Zbl

16 Ira Gessel and D. Stanton: Applications of q-Lagrange inversion to basic hypergeometric series, Trans. Amer. Math. Soc. 277(1) (1983) 173-201. | MR | Zbl

17 H.W. Gould: Combinatorial Identities, Morgantown, West-Virginia, 1972. | MR | Zbl

18 H.W. Gould and L.C. Hsu: Some new inverse series relations, Duke Math. J. 40 (1973) 885-891. | MR | Zbl

19 D.H. Greene and D.E. Knuth: Mathematics for the Analysis of Algorithms, Birkerhauser, 1981. | MR | Zbl

20 C. Krattenthaler: A new matrix inverse, Preprint, 1989. | MR | Zbl

21 B. Nassrallah and M. Rahman: On the q-analogues of some transformations of nearly-poised hypergeometric series, Trans. Amer. Math. Soc. 268 (1981) 211-229. | MR | Zbl

22 M. Rahman: Some cubic summation formulas for basic hypergeometric series, Utilitas Math. 36 (1989) 161-172. | MR | Zbl

23 J. Riordan: Combinatorial Identities, Wiley, New York, 1968. | MR | Zbl

24 L.J. Slater: Generalized Hypergeometric Functions, Cambridge Univ. Press, Cambridge, 1966. | MR | Zbl

25 D. Zeilberger: The method of creative telescoping, Preprint, 1990. | MR | Zbl