Elliptic hypergeometric functions associated with root systems

Preprint English OPEN
Rosengren, Hjalmar; Warnaar, S. Ole;
(2017)
  • Subject: Mathematics - Combinatorics | Mathematical Physics | Mathematics - Classical Analysis and ODEs
    arxiv: Mathematics::Classical Analysis and ODEs

We give a survey of elliptic hypergeometric functions associated with root systems, comprised of three main parts. The first two form in essence an annotated table of the main evaluation and transformation formulas for elliptic hypergeometric integeral and series on roo... View more
  • References (74)
    74 references, page 1 of 8

    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.

    [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.

    [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.

    [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.

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

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

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