Inversion techniques and combinatorial identities. Jackson’s $q$-analogue of the Dougall-Dixon theorem and the dual formulae
Compositio Mathematica, Volume 95 (1995) no. 1, p. 43-68
@article{CM_1995__95_1_43_0,
author = {Chu, Wenchang},
title = {Inversion techniques and combinatorial identities. Jackson's $q$-analogue of the Dougall-Dixon theorem and the dual formulae},
journal = {Compositio Mathematica},
volume = {95},
number = {1},
year = {1995},
pages = {43-68},
zbl = {0847.33004},
mrnumber = {1314696},
language = {en},
url = {http://www.numdam.org/item/CM_1995__95_1_43_0}
}

Chu, Wenchang. Inversion techniques and combinatorial identities. Jackson’s $q$-analogue of the Dougall-Dixon theorem and the dual formulae. Compositio Mathematica, Volume 95 (1995) no. 1, pp. 43-68. http://www.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 525316 | Zbl 0403.33002

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 1441321 | Zbl 0756.33002

3 W.N. Bailey: Generalized Hypergeometric Series, Cambridge University Press, London, 1935. | JFM 61.0406.01 | Zbl 0011.02303

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 938960 | Zbl 0652.10011

5 L. Carlitz: Some inverse relations, Duke Math. J. 40 (1973) 893-901. | MR 337651 | Zbl 0276.05012

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 984548 | Zbl 0666.05007

7 W.C. Chu: Inversion techniques and combinatorial identities: Strange evaluations of basic hypergeometric series, Compositio Math. 9 (1994), 121-144. | Numdam | MR 1273645 | Zbl 0807.33014

8 W.C. Chu: Symmetry on q-Pfaff-Saalschutz-Sheppard series, Rivista di Mat. N11 (1992), 73-79. | MR 1183440 | Zbl 0757.33003

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 1068649 | Zbl 0717.11007

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 708496 | Zbl 0514.33001

12 G. Gasper: Summation, transformation and expansion formulas for bibasic series, Trans. Amer. Math. Soc. 312(1) (1989) 257-277. | MR 953537 | Zbl 0664.33010

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 1043508 | Zbl 0707.33009

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 1052153 | Zbl 0695.33001

15 Ira Gessel and D. Stanton: Strange evaluations of hypergeometric series, SIAM J. Math. Anal. 13 (1982) 295-308. | MR 647127 | Zbl 0486.33003

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 690047 | Zbl 0513.33001

17 H.W. Gould: Combinatorial Identities, Morgantown, West-Virginia, 1972. | MR 354401 | Zbl 0241.05011

18 H.W. Gould and L.C. Hsu: Some new inverse series relations, Duke Math. J. 40 (1973) 885-891. | MR 337652 | Zbl 0281.05008

19 D.H. Greene and D.E. Knuth: Mathematics for the Analysis of Algorithms, Birkerhauser, 1981. | MR 642197 | Zbl 0481.68042

20 C. Krattenthaler: A new matrix inverse, Preprint, 1989. | MR 1291781 | Zbl 0843.15005

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 628455 | Zbl 0469.33004

22 M. Rahman: Some cubic summation formulas for basic hypergeometric series, Utilitas Math. 36 (1989) 161-172. | MR 1030781 | Zbl 0691.33002

23 J. Riordan: Combinatorial Identities, Wiley, New York, 1968. | MR 231725 | Zbl 0194.00502

24 L.J. Slater: Generalized Hypergeometric Functions, Cambridge Univ. Press, Cambridge, 1966. | MR 201688 | Zbl 0135.28101

25 D. Zeilberger: The method of creative telescoping, Preprint, 1990. | MR 1103727 | Zbl 0738.33002