Voir la notice de l'article provenant de la source Math-Net.Ru
@article{AA_2008_20_5_a6, author = {V. P. Spiridonov}, title = {Continuous biorthogonality of the elliptic hypergeometric function}, journal = {Algebra i analiz}, pages = {155--185}, publisher = {mathdoc}, volume = {20}, number = {5}, year = {2008}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/AA_2008_20_5_a6/} }
V. P. Spiridonov. Continuous biorthogonality of the elliptic hypergeometric function. Algebra i analiz, Tome 20 (2008) no. 5, pp. 155-185. http://geodesic.mathdoc.fr/item/AA_2008_20_5_a6/
[1] Andrews G. E., Askey R., Roy R., Special functions, Encyclopedia Math. Appl., 71, Cambridge Univ. Press, Cambridge, 1999 | MR | Zbl
[2] van Diejen J. F., “Integrability of difference Calogero–Moser systems”, J. Math. Phys., 35 (1994), 2983–3004 | DOI | MR | Zbl
[3] Faddeev L. D., “Modular double of a quantum group”, Conference Moshé Flato 1999, vol. I (Dijon), Math. Phys. Stud., 21, Kluwer, Dordrecht, 2000, 149–156 | MR | Zbl
[4] Gorsky A. S., Zabrodin A. V., “Degenerations of Sklyanin algebra and Askey–Wilson polynomials”, J. Phys. A, 26 (1993), L635–L639 | DOI | MR | Zbl
[5] Inozemtsev V. I., “Lax representation with spectral parameter on a torus for integrable particle systems”, Lett. Math. Phys., 17 (1989), 11–17 | DOI | MR | Zbl
[6] Kharchev S., Lebedev D., Semenov-Tian-Shansky M., “Unitary representations of $U_q(sl(2,\mathbb R ))$, the modular double and the multiparticle $q$-deformed Toda chains”, Comm. Math. Phys., 225 (2002), 573–609 | DOI | MR | Zbl
[7] Komori Y., Hikami K., “Quantum integrability of the generalized elliptic Ruijsenaars models”, J. Phys. A, 30 (1997), 4341–4364 | DOI | MR | Zbl
[8] Manin Yu. I., “Sixth Painlevé equation, universal elliptic curve, and mirror of $P^2$”, Geometry of Differential Equations, Amer. Math. Soc. Transl. (2), 186, Amer. Math. Soc., Providence, RI, 1998, 131–151 | MR | Zbl
[9] Rains E. M., “Transformations of elliptic hypergeometric integrals”, Ann. of Math. (2) (to appear)
[10] Rains E. M., “$BC_n$-symmetric Abelian functions”, Duke Math. J., 135 (2006), 99–180 | DOI | MR | Zbl
[11] Rosengren H., “An elementary approach to $6j$-symbols (classical, quantum, rational, trigonometric, and elliptic)”, Ramanujan J., 13 (2007), 131–166 | DOI | MR | Zbl
[12] Rosengren H., “Sklyanin invariant integration”, Int. Math. Res. Not., 2004, no. 60, 3207–3232 | DOI | MR | Zbl
[13] Ruijsenaars S. N. M., “Special functions associated with Calogero–Moser type quantum systems”, Integrable Systems: from Classical to Quantum (Montréal, QC, 1999), CRM Proc. Lecture Notes, 26, Amer. Math. Soc., Providence, RI, 2000, 189–226 | MR | Zbl
[14] Sklyanin E. K., “O nekotorykh algebraicheskikh strukturakh, svyazannykh s uravneniem Yanga–Bakstera”, Funkts. anal. i ego pril., 16:4 (1982), 27–34 | MR | Zbl
[15] Sklyanin E. K., “O nekotorykh algebraicheskikh strukturakh, svyazannykh s uravneniem Yanga–Bakstera. Predstavleniya kvantovoi algebry”, Funkts. anal. i ego pril., 17:4 (1983), 34–48 | MR | Zbl
[16] Spiridonov V. P., “Ob ellipticheskoi beta-funktsii”, Uspekhi mat. nauk, 56:1 (2001), 181–182 | MR | Zbl
[17] Spiridonov V. P., “Theta hypergeometric integrals”, Algebra i analiz, 15:6 (2003), 161–215 | MR | Zbl
[18] Spiridonov V. P., “Derevo Beili dlya integralov”, Teor. i mat. fiz., 139:1 (2004), 104–111 | MR
[19] Spiridonov V. P., Ellipticheskie gipergeometricheskie funktsii, Dokt. dis., LTF OIYaI, 2004, 218 pp.; math.CA/0704.3099
[20] Spiridonov V. P., “Ellipticheskie gipergeometricheskie funktsii i modeli tipa Kalodzhero–Sazerlenda”, Teor. i mat. fiz., 150:2 (2007), 311–324 | MR | Zbl
[21] Takebe T., “Bethe ansatz for higher spin eight-vertex models”, J. Phys. A, 28 (1995), 6675–6706 | DOI | MR | Zbl
[22] Takhtadzhyan L. A., Faddeev L. D., “Kvantovyi metod obratnoi zadachi i $XYZ$ model Geizenberga”, Uspekhi mat. nauk, 34:5 (1979), 13–63 | MR
[23] Zhedanov A. S., “Biorthogonal rational functions and the generalized eigenvalue problem”, J. Approx. Theory, 101 (1999), 303–329 | DOI | MR | Zbl