q-triplicate inverse series relations with applications to q-series

Rocky Mountain Journal of Mathematics

Volumn 35, Issue 4, 2005, Pages 1407-1427

  Zhang, Yusen ^a   Chen, Wei ^a  

^a SHANDONG UNIVERSITY   (China)

Author keywords

Basic hypergeometric series; Q triplicate inverse series relations

Indexed keywords

EID: 29144440108     PISSN: 00357596     EISSN: None     Source Type: Journal    
DOI: 10.1216/rmjm/1181069692     Document Type: Article

References (13)

1. L. Carlitz, Some inverse relations, Duke Math. J. 40 (1973), 45-50.
2. W. Chu, Inversion techniques and combinatorial identities: Balanced hypergeometric series, Rocky Mountain J. Math. 32 (2002), 561-587.
3. W. Chu, Inversion techniques and combinatorial identities, Boll. Un. Mat. Ital. 7 (1993), 737-760.
4. W. Chu, Inversion techniques and combinatorial identities: A unified treatment for the 7F6-series identities, Collect. Math. 45 (1994), 13-43.
5. W. Chu, Basic hypergeometric identities: An introductory revisiting through the Carlitz inversions, Forum Math. 7 (1995), 117-129.
6. G. Gasper and M. Rahman, Basic hypergeometric series, Encyclopedia Math. Appl., vol. 35, Cambridge Univ. Press, Cambridge, 1990.
7. I.M. Gessel and D. Stanton, Application of q-Lagrange inversion to basic hypergeometric series, Trans. Amer. Math. Soc. 277 (1983), 173-203.
8. I.M. Gessel and D. Stanton, Another family of q-Lagrange inversion formulas, Rocky Mountain J. Math. 16 (1986), 373-384.
9. H.W. Gould and L.C. Hsu, Some new inverse series relations, Duke Math. J. 40 (1973), 885-891.
10. L.J. Slater, A new proof of Rogers’s transformations of infinite series, Proc. London Math. Soc. 2 (1951), 460-475.
11. A. Verma and V. K. Jain, Transformations between basic hypergeometric series on different bases and identities of Rogers-Ramanujan type, J. Math. Anal. Appl. 76 (1980), 230-269.
12. Yusen Zhang and Tianming Wang, Applications of Chu’s q-duplicate inverse series relations, submitted.
13. Yusen Zhang and Mingshu Tan, Summation formulae including a 3^2 series, J. Southwest China Norm. Univ. (Natural Science) 5 (2002), 646-651.