Bibliography of Elliptic Hypergeometric Functions

The address of this page is
http://www.math.chalmers.se/~hjalmar/bibliography.html

Compiled by Hjalmar Rosengren. Last updated 19 September 2017.

Elliptic hypergeometric functions first appeared in Date et al. (1988), and more explicitly in Frenkel and Turaev (1997). For an introduction, see Van de Bult (2017), Chapter 11 of Gasper & Rahman (2004), Rosengren (2016) or Spiridonov (2008). When compiling this bibliography, I have restricted myself to publications where elliptic hypergeometric sums or integrals appear explicitly, deliberately excluding many relevant papers on closely related topics.

Please send corrections, additions and comments to hjalmarATchalmersDOTse

I would like to thank Fokko van de Bult, Ilmar Gahramanov, Eric Rains, Michael Schlosser, Slava Spiridonov, Jasper Stokman and Alexei Zhedanov for useful comments.
  1. A. Aggarwal, Dynamical stochastic higher spin vertex models, 1704.02499.
  2. O. Aharony, S. S. Razamat, N. Seiberg and B. Willett, 3d dualities from 4d dualities, J. High Energy Phys. 2013, 149, 1305.3924.
  3. A. Amariti, Integral identities for 3d dualities with SP(2N) gauge groups, 1509.02199.
  4. A. Amariti and C. Klare, A journey to 3d: exact relations for adjoint SQCD from dimensional reduction. J. High Energy Phys. 2015, 148, 1409.8623.
  5. A. A. Ardehali, High-temperature asymptotics of supersymmetric partition functions, J. High Energy Phys. 2016, 025, 1512.03376.
  6. A. A. Ardehali, High-temperature Asymptotics of the 4d Superconformal Index, PhD thesis, University of Michigan, 2016, 1605.06100..
  7. I. Bah, A. Hanany, K. Maruyoshi, S. S. Razamat, Y. Tachikawa and G. Zafrir, 4d N=1 from 6d N=(1,0) on a torus with fluxes, 1702.04740..
  8. V. V. Bazhanov, A. P. Kels and S. M. Sergeev, Comment on star-star relations in statistical mechanics and elliptic gamma function identities, J. Phys. A 46 (2013), 152001, 1301.5775.
  9. V. V. Bazhanov and S. M. Sergeev, A master solution of the quantum Yang-Baxter equation and classical discrete integrable equations, Adv. Theor. Math. Phys. 16 (2012), 65-95, 1006.0651.
  10. V. V. Bazhanov and S. M. Sergeev, Elliptic gamma-function and multi-spin solutions of the Yang-Baxter equation, Nuclear Phys. B 856 (2012), 475-496, 1106.5874.
  11. C. Beem and A. Gadde, The superconformal index of N=1 class S fixed points , J. High Energy Phys. 2014, 36, 1212.1467.
  12. D. Betea, Elliptic Combinatorics and Markov Processes, PhD thesis, California Institute of Technology, 2012.
  13. D. Betea, Elliptically distributed lozenge tilings of a hexagon, 1110.4176.
  14. G. Bhatnagar and M. J. Schlosser, Elliptic well-poised Bailey transforms and lemmas on root systems , 1704.00020.
  15. A. Borodin, V. Gorin and E. M. Rains, q-Distributions on boxed plane partitions, Selecta Math. 16 (2010), 731-789, 0905.0679.
  16. F. Brünner and V. P. Spiridonov, A duality web of linear quivers, 1605.06991.
  17. F. Brünner, D. Regalado and V. P. Spiridonov, Supersymmetric Casimir energy and SL(3,Z) transformations, 1611.03831.
  18. F. van de Bult, Hyperbolic Hypergeometric Functions, PhD thesis, University of Amsterdam, 2007.
  19. F. J. van de Bult, An elliptic hypergeometric integral with W(F4) symmetry, Ramanujan J. 25 (2011), 1-20, 0909.4793.
  20. F. J. van de Bult, Elliptic hypergeometric functions, in D. Levi et al. (eds.), Symmetries and Integrability of Difference Equations, Springer, 2017.
  21. F. J. van de Bult, An elliptic hypergeometric beta integral transformation, 0912.3812.
  22. F. J. van de Bult, Two multivariate quadratic transformations of elliptic hypergeometric integrals, 1109.1123.
  23. F. J. van de Bult, More basic hypergeometric limits of the elliptic hypergeometric beta integral, 1307.2458.
  24. F. J. van de Bult and E. M. Rains, Basic hypergeometric functions as limits of elliptic hypergeometric functions, SIGMA 5 (2009), 059, 0902.0621.
  25. F. J. van de Bult and E. M. Rains, Limits of elliptic hypergeometric biorthogonal functions, J. Approx. Theory 193 (2015), 128-163, 1110.1456.
  26. F. J. van de Bult and E. M. Rains, Limits of multivariate elliptic hypergeometric biorthogonal functions, 1110.1458.
  27. F. J. van de Bult and E. M. Rains, Limits of multivariate elliptic beta integrals and related bilinear forms, 1110.1460.
  28. F. J. van de Bult, E. M. Rains and J. V. Stokman, Properties of generalized univariate hypergeometric functions, Comm. Math. Phys. 275 (2007), 37-95, math/0607250.
  29. H.-Y. Chen and H.-Y. Chen, Heterotic surface defects and dualities from 2d/4d indices, 1407.4587.
  30. S. H. L. Chen and A. M. Fu, A 4n-point elliptic interpolation formula and its applications, SIAM J. Discrete Math. 31 (2017), 758-765.
  31. D. Chicherin, S. E. Derkachov and V. P. Spiridonov, New elliptic solutions of the Yang-Baxter equation, Comm. Math. Phys. 345 (2016), 507-543, 1412.3383.
  32. W. Chu and C. Jia, Abel's method on summation by parts and theta hypergeometric series, J. Combin. Theory Ser. A 115 (2008), 815-844.
  33. W. Chu and C. Jia, Abel's method on summation by parts for elliptic hypergeometric series, Commun. Contemp. Math. 11 (2009), 337-353.
  34. W. Chu and C. Jia, Quartic theta hypergeometric series, Ramanujan J. 32 (2013), 23-81.
  35. H. Coskun, An elliptic BCn Bailey lemma, multiple Rogers-Ramanujan identities and Euler's pentagonal number theorems, Trans. Amer. Math. Soc. 360 (2008), 5397-5433, math/0605653.
  36. H. Coskun and R. A. Gustafson, Well-poised Macdonald functions Wλ and Jackson coefficients ωλ on BCn, in V. B. Kuznetsov and S. Sahi (eds.), Jack, Hall-Littlewood and Macdonald polynomials, Contemp. Math. 417, Amer. Math. Soc., Providence, 2006, pp. 127-155, math/0412153.
  37. E. Date, M. Jimbo, A. Kuniba, T. Miwa, and M. Okado, Exactly solvable SOS models. II. Proof of the star-triangle relation and combinatorial identities, in M. Jimbo et al. (eds.), Conformal Field Theory and Solvable Lattice Models, Academic Press, Boston, 1988, pp. 17-122.
  38. R. Y. Denis, S. N. Singh and S. P. Singh, On transformation formulas for theta hypergeometric functions, Ukrainian Math. J. 64 (2012), 1136-1143.
  39. S. Derkachov, D. Karakhanyan and R. Kirschner, Yang-Baxter R-operators and parameter permutations, Nuclear Physics B 785 (2007), 263-285, hep-th/0703076.
  40. S. E. Derkachov and V. P. Spiridonov, The Yang-Baxter equation, parameter permutations, and the elliptic beta integral, Russian Math. Surveys 68 (2013), 1027-1072, 1205.3520.
  41. S. E. Derkachov and V. P. Spiridonov, Finite dimensional representations of the elliptic modular double, Theoret. and Math. Phys. 183 (2015), 597-618, 1310.7570.
  42. J. F. van Diejen and V. P. Spiridonov, An elliptic Macdonald-Morris conjecture and multiple modular hypergeometric sums, Math. Res. Lett. 7 (2000), 729-746.
  43. J. F. van Diejen and V. P. Spiridonov, Elliptic Selberg integrals, Internat. Math. Res. Notices 2001 (2001), 1083-1110.
  44. J. F. van Diejen and V. P. Spiridonov, Modular hypergeometric residue sums of elliptic Selberg integrals Lett. Math. Phys. 58 (2001), 223-238.
  45. J. F. van Diejen and V. P. Spiridonov, Elliptic beta integrals and modular hypergeometric sums: an overview, Rocky Mountain J. Math. 32 (2002), 639-656.
  46. J. F. van Diejen and V. P. Spiridonov, Unit circle elliptic beta integrals , Ramanujan J. 10 (2005), 187-204, math/0309279.
  47. T. Dimofte and D. Gaiotto, An E7 surprise, J. High Energy Phys. 2012, 129, 1209.1404.
  48. F. A. Dolan and H. Osborn, Applications of the superconformal index for protected operators and q-hypergeometric identities to N=1 dual theories, Nucl. Phys. B 818 (2009), 137-178, 0801.4947.
  49. F. A. H. Dolan, V. P. Spiridonov and G. S. Vartanov, From 4d superconformal indices to 3d partition functions, Phys. Lett. B 704 (2011), 234-241, 1104.1787.
  50. P. J. Forrester and S. O. Warnaar, The importance of the Selberg integral, Bull. Amer. Math. Soc. 45 (2008), 489-534, 0710.3981.
  51. S. Franco, H. Hayashi and A. Uranga, Charting class Sk territory, Phys. Rev. D 92 (2015), 045004, 1504.05988.
  52. I. B. Frenkel and V. G. Turaev, Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions, in V. I. Arnold et al. (eds.), The Arnold-Gelfand Mathematical Seminars, Birkhäuser, Boston, 1997, pp. 171-204.
  53. A. Gadde and S. Gukov, 2d index and surface operators, J. High. Energy Phys. 2014, 80, 1305.0266.
  54. A. Gadde, E. Pomoni, L. Rastelli and S. S. Razamat, S-duality and 2d topological QFT, J. High Energy Phys. 2010, 032, 0910.2225.
  55. A. Gadde, L. Rastelli, S. S. Razamat and W. Yan, The superconformal index of the E6 SCFT, J. High Energy Phys. 2010, 107, 1003.4244.
  56. A. Gadde, L. Rastelli, S. S. Razamat and W. Yan, On the superconformal index of N = 1 IR fixed points: a holographic check, J. High Energy Phys. 2011, 041, 1011.5278.
  57. I. Gahramanov, Mathematical structures behind supersymmetric dualities, Arch. Math. (Brno) 51 (2015), 273-286, 1505.05656.
  58. I. Gahramanov, Superconformal Indices, Dualities and Integrability, PhD thesis, Humboldt-Universität zu Berlin, 2016.
  59. I. Gahramanov and A. P. Kels, The star-triangle relation, lens partition function, and hypergeometric sum/integrals, 1610.09229.
  60. I. Gahramanov and G. Vartanov, Extended global symmetries for 4D N=1 SQCD theories, J. Phys. A. 46 (2013), 285403, 1303.1443.
  61. I. B. Gahramanov and G. S. Vartanov, Superconformal indices and partition functions for supersymmetric field theories, in XVIIth International Congress on Mathematical Physics, World Sci. Publ., Hackensack, 2014, 605-703, 1310.8507.
  62. D. Gaiotto and H.-C. Kim, Surface defects and instanton partition functions, J. High Energy Phys. 2016, 012, 1412.2781.
  63. D. Gaiotto, L. Rastelli and S. S. Razamat, Bootstrapping the superconformal index with surface defects, J. High Energy Phys. 2013, 022, 1207.3577.
  64. D. Gaiotto and S. S. Razamat, N=1 theories of class Sk, J. High Energy Phys. 2015, 073, 1503.05159.
  65. I. García-Extebarria, B. Heidenreich and T. Wrase, New N=1 dualities from orientifold transitions - Part I: Field theory, J. High Energy Phys. 2013, 007, 1210.7799.
  66. G. Gasper and M. Rahman, Basic Hypergeometric Series, Second edition, Cambridge University Press, Cambridge, 2004.
  67. G. Gasper and M. J. Schlosser, Summation, transformation, and expansion formulas for multibasic theta hypergeometric series, Adv. Stud. Contemp. Math. (Kyungshang) 11 (2005), 67-84; also published in M. Noumi and K. Takasaki (eds.), Elliptic Integrable Systems, Rokko Lectures in Math. 18, Kobe University, 2005, pp. 1-17, math/0505215.
  68. M. Ito and M. Noumi, Derivation of a BCn elliptic summation formula via the fundamental invariants, Constr. Approx. 45 (2017), 33-46, 1504.07108.
  69. M. Ito and M. Noumi, Evaluation of the BCn elliptic Selberg integrals via the fundamental invariants, Proc. Amer. Math. Soc. 145 (2017), 689-703, 1504.07317.
  70. Y. Kajihara, Symmetry groups of An hypergeometric series, SIGMA 10 (2014), 026, 1310.7273.
  71. Y. Kajihara and M. Noumi, Multiple elliptic hypergeometric series. An approach from the Cauchy determinant, Indag. Math. 14 (2003), 395-421, math/0306219.
  72. K. Kajiwara, T. Masuda, M. Noumi, Y. Ohta and Y. Yamada, 10E9 solution to the elliptic Painlevé equation, J. Phys. A 36 (2003), L263-L272, nlin/0303032.
  73. K. Kashaev, F. Luo and G. Vartanov, A TQFT of Turaev-Viro type on shaped triangulations, Ann. Henri Poincaré 17 (2016),1109-1143, 1210.8393.
  74. A. P. Kels, New solutions of the star-triangle relation with discrete and continuous spin variables, J. Phys. A 48 (2015), 435201, 1504.07074.
  75. A. P. Kels and M. Yamazaki, Elliptic hypergeometric sum/integral transformations and supersymmetric lens index, 1704.03159.
  76. E. Koelink and Y. van Norden, Pairings and actions for dynamical quantum groups, Adv. Math. 208 (2007), 1-39, math/0412205.
  77. E. Koelink, Y. van Norden, and H. Rosengren, Elliptic U(2) quantum group and elliptic hypergeometric series, Comm. Math. Phys. 245 (2004), 519-537, math/0304189.
  78. Y. Komori, Elliptic Ruijsenaars operators and elliptic hypergeometric integrals, in M. Noumi and K. Takasaki (eds.), Elliptic Integrable Systems, Rokko Lectures in Math. 18, Kobe University, 2005, pp. 49-56.
  79. Y. Komori, Y. Masuda and M. Noumi, Duality transformation formulas for multiple elliptic hypergeometric series of type BC, Constr. Approx. 44 (2016), 483-516, 1410.6921.
  80. H. Konno, The vertex-face correspondence and the elliptic 6j-symbols , Lett. Math. Phys. 72 (2005), 243-258, math/0503725.
  81. H. Konno, Generalized elliptic 6j-symbols in terms of the vertex-face intertwining vectors, in M. Noumi and K. Takasaki (eds.), Elliptic Integrable Systems, Rokko Lectures in Math. 18, Kobe University, 2005, pp. 57-69.
  82. H. Konno, Elliptic quantum group Uq,p(\hat{sl}2), Hopf algebroid structure and elliptic hypergeometric series, J. Geom. Phys. 59 (2009), 1485-1511, 0803.2292.
  83. A. Korovnichenko, V. P. Spiridonov and A. S. Zhedanov, Poisson algebras on elliptic curves, Pr. Inst. Mat. Nats. Akad. Nauk Ukr. Mat. Zastos. 50 (2004), 1116-1123 (or 1116-1125?).
  84. C. Krattenthaler and M. J. Schlosser, The major index generating function of standard Young tableaux of shapes of the form "staircase minus rectangle", in K. Alladi et al. (eds.), Ramanujan 125, Contemp. Math. 627, Amer. Math. Soc., Providence, 2014, pp. 111-122, 1402.4538.
  85. D. Kutasov and J. Lin, N=1 Duality and the Superconformal Index, 1402.5411.
  86. R. Langer, M. J. Schlosser and S. O. Warnaar, Theta functions, elliptic hypergeometric series, and Kawanaka's Macdonald polynomial conjecture, SIGMA 5 (2009), 055, 0905.4033.
  87. A. P. Magnus, Elliptic hypergeometric solutions to elliptic difference equations, SIGMA 5 (2009), 038, 0903.4803.
  88. K. Maruyoshi and J. Yagi, Surface defects as transfer matrices, 1606.01041.
  89. V. Niarchos, Seiberg dualities and the 3d/4d connection, J. High Energy Phys. 2012, 75, 1205.2086.
  90. F. Nieri, An elliptic Virasoro symmetry in 6d, 1511.00574.
  91. F. Nieri and S. Pasquetti, Factorisation and holomorphic blocks in 4d, J. High Energy Phys. 2015, 155, 1507.00261.
  92. Y. van Norden, Dynamical Quantum Groups, Duality and Special Functions, PhD thesis, Delft University of Technology, 2005.
  93. M. Noumi, Padé interpolation and hypergeometric series, in A. Dzhamay, K. Maruno and C. M. Ormerod (eds.), Algebraic and Analytic Aspects of Integrable Systems and Painlevé Equations, Contemp. Math. 651, Amer. Math. Soc., Providence, 2015, pp. 1-23. 1503.02147.
  94. M. Noumi, Remarks on τ-functions for the difference Painlevé equations of type E8, 1604.06869.
  95. M. Noumi, S. Tsujimoto and Y. Yamada, Padé interpolation for elliptic Painlevé equation, in K. Iohara et al. (eds.), Symmetries, Integrable Systems and Representations, Springer-Verlag, London, 2013, pp. 463-482, 1204.0294.
  96. W. Peelaers, Higgs branch localization of N=1 theories on S3 x S1, J. High. Energy Phys. 2014, 30, 1403.2711.
  97. E. M. Rains, Recurrences for elliptic hypergeometric integrals, in M. Noumi and K. Takasaki (eds.), Elliptic Integrable Systems, Rokko Lectures in Math. 18, Kobe University, 2005, pp. 183-199, math/0504285.
  98. E. M. Rains, BCn-symmetric abelian functions, Duke Math. J. 135 (2006), 99-180, math/0402113.
  99. E. M. Rains, Limits of elliptic hypergeometric integrals, Ramanujan J. 18 (2009), 257-306, math/0607093.
  100. E. M. Rains, Transformations of elliptic hypergeometric integrals, Ann. Math. 171 (2010), 169-243, math/0309252.
  101. E. M. Rains, Elliptic analogues of the Macdonald and Koornwinder polynomials, in Proceedings of the International Congress of Mathematicians, Vol. IV, Hindustan Book Agency, New Delhi, 2010, pp. 2530-2554.
  102. E. M. Rains, An isomonodromy interpretation of the hypergeometric solution of the elliptic Painlevé equation (and generalizations), SIGMA 7 (2011), 088, 0807.0258.
  103. E. M. Rains, Elliptic Littlewood identities, J. Combin. Theory A 119 (2012), 1558-1609, 0806.0871.
  104. E. M. Rains, Generalized Hitchin systems on rational surfaces, 1307.4033.
  105. E. M. Rains, Multivariate quadratic transformations and the interpolation kernel, 1408.0305.
  106. E. M. Rains, The noncommutative geometry of elliptic difference equations, 1607.08876.
  107. E. M. Rains and V. P. Spiridonov, Determinants of elliptic hypergeometric integrals, Func. Anal. Appl. 43 (2009), 297-311, 0712.4253.
  108. E. M. Rains, Y. Sun and A. Varchenko, Affine Macdonald conjectures and special values of Felder-Varchenko functions, 1610.01917.
  109. L. Rastelli and S. S. Razamat, The superconformal index of theories of class S, in J. Teschner (ed.), New Dualities of Supersymmetric Gauge Theories, Springer, Cham, 2016, pp. 261-305. 1412.7131.
  110. L. Rastelli and S. S. Razamat, The supersymmetric index in four dimensions, 1608.02965.
  111. S. S. Razamat, On the N=2 superconformal index and eigenfunctions of the elliptic RS model, Lett. Math. Phys. 104 (2014), 673-690, 1309.0278.
  112. S. S. Razamat, C. Vafra and G. Zafrir, 4d N=1 from 6d (1,0), 1610.09178.
  113. S. S. Razamat and B. Willett, Global properties of supersymmetric theories and the lens space, Comm. Math. Phys. 334 (2015), no. 2, 661-696, 1307.4381.
  114. H. Rosengren, 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, Amer. Math. Soc., Providence, 2001, pp. 193-202, math/0101073.
  115. H. Rosengren, Elliptic hypergeometric series on root systems, Adv. Math. 181 (2004), 417-447, math/0207046.
  116. H. Rosengren, Sklyanin invariant integration, Int. Math. Res. Not. 2004 (2004), 3207-3232, math/0405072.
  117. H. Rosengren, An elliptic determinant transformation, in M. Noumi and K. Takasaki (eds.), Elliptic Integrable Systems, Rokko Lectures in Math. 18, Kobe University, 2005, pp. 241-246, math/0505248.
  118. H. Rosengren, New transformations for elliptic hypergeometric series on the root system An, Ramanujan J. 12 (2006), 155-166, math/0305379.
  119. H. Rosengren, An elementary approach to 6j-symbols (classical, quantum, rational, trigonometric, and elliptic), Ramanujan J. 13 (2007), 133-168, math/0312310.
  120. H. Rosengren, Felder's elliptic quantum group and elliptic hypergeometric series on the root system An, Int. Math. Res. Not. 2011 (2011), 2861-2920, 1003.3730.
  121. H. Rosengren, Elliptic hypergeometric functions, 1608.06161.
  122. H. Rosengren, Gustafson-Rakha-type elliptic hypergeometric series, 1701.08960.
  123. H. Rosengren and M. Schlosser, Summations and transformations for multiple basic and elliptic hypergeometric series by determinant evaluations, Indag. Math. 14 (2003), 483-514, math/0304249.
  124. H. Rosengren and M. Schlosser, On Warnaar's elliptic matrix inversion and Karlsson-Minton-type elliptic hypergeometric series, J. Comput. Appl. Math. 178 (2005), 377-391, math/0309358.
  125. H. Rosengren and S. O. Warnaar, Elliptic hypergeometric functions associated with root systems, 1704.08406.
  126. M. J. Schlosser, Elliptic enumeration of nonintersecting lattice paths, J. Combin. Theory A 114 (2007), 505-521, math/0602260.
  127. M. J. Schlosser, A Taylor expansion theorem for an elliptic extension of the Askey-Wilson operator, in D. Dominici and R. S. Maier (eds.), Special Functions and Orthogonal Polynomials, Contemp. Math. 471, Amer. Math. Soc., Providence, 2008, pp. 175-186, 0803.2329.
  128. M. J. Schlosser, A noncommutative weight-dependent generalization of the binomial theorem, 1106.2112.
  129. M. J. Schlosser and M. Yoo, Elliptic hypergeometric summations by Taylor series expansion and interpolation, SIGMA 12 (2016), 039, 1602.09027.
  130. S. P. Singh and A. K. Singh, On a transformation formula for elliptic hypergeometric series, South East Asian J. Math. Math. Sci. 10 (2011), 79-88.
  131. V. P. Spiridonov, Solitons and Coulomb plasmas, similarity reductions and special functions, in C. Dunkl et al. (eds.), Special Functions, World Scientific, River Edge, 2000, pp. 324-338.
  132. V. P. Spiridonov, On the elliptic beta function, Russian Math. Surveys 56 (2001), 185-186.
  133. V. P. Spiridonov, New special functions of hypergeometric type and elliptic beta integrals (in Russian), Phys. Part. Nucl. 32 (2001), 88--92.
  134. V. P. Spiridonov, Elliptic beta integrals and special functions of hypergeometric type, in G. von Gehlen and S. Pakuliak (eds.), Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory, Kluwer, Dordrecht, 2001, pp. 305-313.
  135. V. P. Spiridonov, Theta hypergeometric series, in V.A. Malyshev and A.M. Vershik (eds.), Asymptotic Combinatorics with Applications to Mathematical Physics, Kluwer, Dordrecht, 2002, pp. 307-327, math/0303204.
  136. V. P. Spiridonov, An elliptic beta integral, in S. Elaydi et al. (eds.), New Trends in Difference Equations, Taylor & Francis, London, 2002, pp. 273-282.
  137. V. P. Spiridonov, An elliptic incarnation of the Bailey chain, Int. Math. Res. Not. 2002 (2002), 1945-1977.
  138. V. P. Spiridonov, Modularity and total ellipticity of some multiple series of hypergeometric type, Theor. Math. Phys. 135 (2003), 836-848.
  139. V. P. Spiridonov, Theta hypergeometric integrals, St. Petersburg Math. J. 15 (2004), 929-967, math/0303205.
  140. V. P. Spiridonov, A Bailey tree for integrals, Theor. Math. Phys. 139 (2004), 536-541, math/0312502.
  141. V. P. Spiridonov, Elliptic Hypergeometric Functions (in Russian), Habilitation Thesis, JINR, Dubna, 2004, 1610.01557.
  142. V. P. Spiridonov, Classical elliptic hypergeometric functions and their applications, in M. Noumi and K. Takasaki (eds.), Elliptic Integrable Systems, Rokko Lectures in Math. 18, Kobe University, 2005, pp. 253-287, math/0511579.
  143. V. P. Spiridonov, A multiparameter summation formula for Riemann theta functions, in V. B. Kuznetsov and S. Sahi (eds.), Jack, Hall-Littlewood and Macdonald polynomials, Contemp. Math. 417, Amer. Math. Soc., Providence, 2006, pp. 345-353, math/0408366.
  144. V. P. Spiridonov, Short proofs of the elliptic beta integrals, Ramanujan J. 13 (2007), 265-283, math/0408369.
  145. V. P. Spiridonov, Elliptic hypergeometric functions and Calogero-Sutherland-type models, Theor. Math. Phys 150 (2007), 266-277.
  146. V. P. Spiridonov, Essays on the theory of elliptic hypergeometric functions, Russian Math. Surveys 63 (2008), 405-472, 0805.3135.
  147. V. P. Spiridonov, Continuous biorthogonality of the elliptic hypergeometric function, St. Petersburg Math. J. 20 (2009), 791-812, 0801.4137.
  148. V. P. Spiridonov, Elliptic hypergeometric terms, SNF Séminaire et Congrès 23 (2011), 385-405, 1003.4491.
  149. V. P. Spiridonov, Elliptic beta integrals and solvable models of statistical mechanics, in P. B. Acosta-Humánez et al. (eds.), Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics, Contemp. Math. 563, Amer. Math. Soc., Providence, 2012, pp. 345-353, 1011.3798.
  150. V. P. Spiridonov, Modified elliptic gamma functions and 6d superconformal indices, Lett. Math. Phys. 104 (2014), 397-414, 1211.2703.
  151. V. P. Spiridonov, An elliptic analogue of the Gauss hypergeometric function, preprint, MPIM2007-75 (2007).
  152. V. P. Spiridonov, Elliptic hypergeometric functions, complement to the Russian edition of G. E. Andrews, R. Askey, and R. Roy, Special Functions, 0704.3099.
  153. V. P. Spiridonov, Aspects of elliptic hypergeometric functions, in B. C. Berndt and D. Prasad (eds.), The legacy of Srinivasa Ramanujan, Ramanujan Math. Soc., Mysore, 2013, pp. 347-361, 1307.2876.
  154. V. P. Spiridonov, Rarefied elliptic hypergeometric functions, 1609.00715.
  155. V. P. Spiridonov and G. S. Vartanov, Superconformal indices for N=1 theories with multiple duals, Nucl. Phys.B 824 (2010), 192-216, 0811.1909.
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