# Elliptic hypergeometric functions associated with root systems

- Published: 26 Apr 2017

R∗λ(x1, . . . , xn+1; a, b; q, t; p) = X cλμ(xn+1; a, b; q, t, tn; p)R∗μ(x1, . . . , xn; a, b; q, t; p), (1.4.3) μ

[1] Askey, R. and Wilson J. 1985. Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Memoirs Amer. Math. Soc., 54. [OpenAIRE]

[2] Bazhanov, V. V., Kels A. P. and Sergeev S. M. 2013. Comment on star-star relations in statistical mechanics and elliptic gamma function identities. J. Phys. A, 46, 152001. [OpenAIRE]

[3] Bazhanov, V. V. and Sergeev, S. M. 2012. A master solution of the quantum Yang-Baxter equation and classical discrete integrable equations, Adv. Theor. Math. Phys., 16 65-95. [OpenAIRE]

[4] Bazhanov, V. V. and Sergeev, S. M. 2012. Elliptic gamma-function and multi-spin solutions of the Yang-Baxter equation. Nucl. Phys. B, 856, 475-496.

[5] Bhatnagar, G. 1999. Dn basic hypergeometric series. Ramanujan J., 3, 175-203.

[6] Bhatnagar, G. and Schlosser, M. 1998. Cn and Dn very-well-poised 10φ9 transformations. Constr. Approx., 14, 531-567.

[7] Bhatnagar, G. and Schlosser, M. 2017. Elliptic well-poised Bailey transforms and lemmas on root system. arXiv:1704.00020. [OpenAIRE]

[8] van de Bult, F. J. 2009. An elliptic hypergeometric beta integral transformation. arXiv:0912.3812. [OpenAIRE]

[9] van de Bult, F. J. 2011. Two multivariate quadratic transformations of elliptic hypergeometric integrals. arXiv:1109.1123. [OpenAIRE]

[10] Coskun, H. and Gustafson, R. A. 2006. Well-poised Macdonald functions Wλ and Jackson coefficients ωλ on BCn. Pages 127-155 of: V. B. Kuznetsov and S. Sahi (eds.), Jack, Hall-Littlewood and Macdonald polynomials, Contemp. Math., 417, Amer. Math. Soc.

[11] Coskun, H. 2008. An elliptic BCn Bailey lemma, multiple Rogers-Ramanujan identities and Euler's pentagonal number theorems. Trans. Amer. Math. Soc., 360, 5397-5433.

[12] Date, E., Jimbo, M., Kuniba, A., Miwa, T. and Okado, M. 1988. Exactly solvable SOS models. II. Proof of the star-triangle relation and combinatorial identities. Pages 17- 122 of: M. Jimbo et al. (eds.), Conformal Field Theory and Solvable Lattice Models, Academic Press. [OpenAIRE]

[13] Denis, R. Y. and Gustafson, R. A. 1992. An SU(n) q-beta integral transformation and multiple hypergeometric series identities. SIAM J. Math. Anal., 23, 552-561.

[14] van Diejen, J. F. and Spiridonov, V. P. 2000. An elliptic Macdonald-Morris conjecture and multiple modular hypergeometric sums. Math. Res. Lett., 7, 729-746.