Some new applications of matrix inversions in Ar

Ramanujan Journal

Volumn 3, Issue 4, 1999, Pages 405-461

  Schlosser, Michael ^a,b  

^a UNIVERSITY OF VIENNA   (Austria)

^b OHIO STATE UNIVERSITY   (United States)

Author keywords

Multidimensional matrix inversions; Multiple q series associated to the root systems Ar and Dr, U(n + 1) series; Terminating and nonterminating Ar q Abel summations

Indexed keywords

EID: 22844454624     PISSN: 13824090     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1009809424076     Document Type: Article

References (17)

1. G.E. Andrews, "Connection coefficient problems and partitions," in Proc. Symp. Pure Math. (D. Ray-Chaudhuri, ed.), Vol. 34, Amer. Math. Soc., Providence, R.I., 1979, 1-24.
2. W.N. Bailey, "Some identities in combinatory analysis," Proc. London Math. Soc. 49(2) (1947), 421-435.
3. G. Bhatnagar, "Inverse relations, generalized bibasic series and their U(n) extensions," Ph.D. thesis, The Ohio State University, 1995.
4. n basic hypergeometric series," The Ramanujan J. 3 (1999), 175-203.
5. G. Bhatnagar and S.C. Milne, "Generalized bibasic hypergeometric series and their U(n) extensions," Adv. m Math. 131(1997), 188-252.
6. n very-well-poised 10φ9 transformations," Constr. Approx. 14 (1998), 531-567.
7. D.M. Bressoud, "A matrix inverse," Proc. Amer. Math. Soc. 88 (1983), 446-448.
8. L. Carlitz, "Some inverse relations," Duke Math. J. 40 (1973), 893-901.
9. L. Carlitz, "Some expansions and convolution formulas related to MacMahon's Master Theorem," SIAM J. Appl. Math. 8 (1977), 320-336.
10. W. Chu, "Some multifold reciprocal transformations with applications to series expansions," Europ. J. Comb. 12(1991), 1-8.
11. W. Chu, "Inversion techniques and combinatorial identities - Jackson's q-analogue of the Dougall-Dixon theorem and the dual formulae," Compositio Math. 95 (1995), 43-68.
12. J.F. van Diejen, "On certain multiple Bailey, Rogers and Dougall type summation formulas," Publ. RIMS, Kyoto Univ. 33 (1997), 483-508.
13. L. Euler, De serie Lambertiana plurimisque eius insignibus proprietatibus, reprinted in Opera Omnia Ser. I 6, Teubner, Leibzig, 1921, pp. 350-369.
14. G. Gasper, "Summation, transformation and expansion formulas for bibasic series," Trans. Amer. Soc. 312 (1989), 257-278.
15. G. Gasper and M. Rahman, "An indefinite bibasic summation formula and some quadratic, cubic and quartic summation and transformation formulae," Canad. J. Math. 42 (1990a), 1-27.
16. G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990(b).
17. I.M. Gessel and D. Stanton, "Application of q-Lagrange inversion to basic hypergeometric series," Trans. Amer. Math. Soc. 277 (1983), 173-203.