Summations and transformations for multiple basic and elliptic hypergeometric series by determinant evaluations

Indagationes Mathematicae

Volumn 14, Issue 3-4, 2003, Pages 483-513

  Rosengren, Hjalmar ^a   Schlosser, Michael ^b  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

^b UNIVERSITY OF VIENNA   (Austria)

Author keywords

10 9 transformations; 1 1 summations; 8 7 summations; Ar 1 series; Basic hypergeometric series; Cr series; Elliptic hypergeometric series; Multiple q integrals

Indexed keywords

EID: 1042291519     PISSN: 00193577     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0019-3577(03)90058-9     Document Type: Article

References (27)

1. Andrews, G.E. - Applications of basic hypergeometric functions. SIAM Rev. 16 441-484 (1974).
2. Andrews, G.E. - q-Series: Their development and application in analysis, number theory, combinatorics, physics and computer algebra. CBMS Regional Conference Lectures Series 66 (Amer. Math. Soc., Providence, RI, 1986).
3. Andrews, G.E., R. Askey and R. Roy - Special functions. Encyclopedia of Mathematics And Its Applications, Vol. 71, Cambridge University Press, Cambridge (1999).
4. Bailey, W. N. - An identity involving Heine's basic hypergeometric series. J. London Math. Soc. 4 254-257 (1929).
5. Bailey, W.N. - Well-poised basic hypergeometric series. Quart. J. Math. (Oxford) 18 157-166 (1947).
6. n basic hypergeometric series. The Ramanujan J. 3 175-203 (1999).
7. Denis, R.Y. and R.A. Gustafson - An SU(n) q-beta integral transformation and multiple hypergeometric series identities. SIAM J. Math. Anal. 23 552-561 (1992).
8. van Diejen, J.F. and V.P. Spiridonov - An elliptic Macdonald-Morris conjecture and multiple modular hypergeometric sums. Math. Res. Lett. 7 729-746 (2000).
9. van Diejen, J.F. and V.P. Spiridonov - Modular hypergeometric residue sums of elliptic Selberg integrals. Lett. Math. Phys. 58 223-238 (2001).
10. Frenkel, I.B. and V.G. Turaev - Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions. in: V.I. Arnold, I.M. Gelf and, V.S. Retakh and M. Smirnov (Eds.), The Arnold-Gelfand mathematical seminars, Birkhäuser, Boston, pp. 171-204 (1997).
11. Gasper, G. and M. Rahman - Basic hypergeometric series. Encyclopedia of Mathematics And Its Applications, Vol. 35, Cambridge University Press, Cambridge, (1990).
12. 1-transformations. in: M.E.H. Ismail, D.R. Masson and M. Rahman (Eds.), Special functions, q-series and related topics, Amer. Math. Soc., Providence, R. I., Fields Institute Communications 14 83-90 (1997).
13. Hardy, G.H. - Ramanujan. Cambridge University Press, Cambridge (1940); Chelsea, New York (1978).
14. Holman, W.J., L.C. Biedenharn, and J.D. Louck - On hypergeometric series well-poised in SU(n). SIAM J. Math. Anal. 7 529-541 (1976).
15. Jackson, F.H. - On q-definite integrals. Quart. J. Pure Appl. Math. 41 193-203 (1910).
16. Jackson, F.H. - Summation of q-hypergeometric series. Messenger of Math. 57 101-112 (1921).
17. Krattenthaler, C. -The major counting of nonintersecting lattice paths and generating functions for tableaux. Mem. Amer. Math. Soc. 115, no. 552 (1995).
18. Milne, S.C. - Transformations of U(n + 1) multiple basic hypergeometric series. in: A.N. Kirillov, A. Tsuchiya, and H. Umemura (Eds.), Physics and combinatorics: Proceedings of the Nagoya 1999 international workshop (Nagoya University, Japan, August 23-27, 1999), World Scientific, Singapore, pp. 201-243 (2001).
19. 9 transformations. J. Comput. Appl. Math. 68 239-285 (1996).
20. n-symmetric polynomials. preprint, arXiv:math.QA/0112035.
21. Rosengren, H. - A proof of a multivariable elliptic summation formula conjectured by Warnaar. in: B. C. Berndt and K. Ono (Eds.), q-Series with applications to combinatorics, number theory and physics. Contemp. Math. 291, pp. 193-202 (2001).
22. Rosengren, H. - Elliptic hypergeometric series on root systems. Adv. Math., to appear.
23. Schlosser, M. - Summation theorems for multidimensional basic hypergeometric series by determinant evaluations. Discrete Math. 210 151-169 (2000).
24. r. J. Comput. Appl. Math., to appear.
25. Spiridonov, V.P. - Theta hypergeometric series. in: V. A. Malyshev and A. M. Vershik (Eds.), Asymptotic combinatorics with applications to mathematical physics, Kluwer Acad. Publ., Dordrecht, pp. 307-327 (2002).
26. Spiridonov, V.P. - Theta hypergeometric integrals. preprint, arXiv: math. CA/0303205.
27. Warnaar, S.O. - Summation and transformation formulas for elliptic hypergeometric series. Constr. Approx. 18 479-502 (2002).