-
1
-
-
0004167330
-
-
Encyclopedia Math. Appl, Cambridge Univ. Press, Cambridge
-
G.E. Andrews, R. Askey, and R. Roy, Special functions, Encyclopedia Math. Appl., vol. 71, Cambridge Univ. Press, Cambridge 1999.
-
(1999)
Special functions
, vol.71
-
-
Andrews, G.E.1
Askey, R.2
Roy, R.3
-
2
-
-
84956086202
-
General hypergeometric systems of equations and series of hypergeometric type
-
English transl., I. M. Gel'fand, M. I. Graev, and V. S. Retakh, "General hypergeometric systems of equations and series of hypergeometric type", Russian Math. Surveys 47:4 (1992), 1-88.
-
(1992)
Russian Math. Surveys
, vol.47
, Issue.4
, pp. 1-88
-
-
English transl, I.1
Gel'fand, M.2
Graev, M.I.3
Retakh, V.S.4
-
3
-
-
0004216016
-
-
2nd ed, Encyclopedia Math. Appl, Cambridge Univ. Press, Cambridge
-
G. Gasper and M. Rahman, Basic hypergeometric series, 2nd ed., Encyclopedia Math. Appl., vol. 96, Cambridge Univ. Press, Cambridge 2004.
-
(2004)
Basic hypergeometric series
, vol.96
-
-
Gasper, G.1
Rahman, M.2
-
4
-
-
1442347924
-
Quantum inverse problem method. I
-
English transl., E. K. Sklyanin, L. A. Takhtadzhyan, and L. D. Faddeev, "Quantum inverse problem method. I", Theoret. Math. Phys. 40:2 (1979), 688-706.
-
(1979)
Theoret. Math. Phys
, vol.40
, Issue.2
, pp. 688-706
-
-
English transl, E.1
Sklyanin, K.2
Takhtadzhyan, L.A.3
Faddeev, L.D.4
-
5
-
-
84901244244
-
The quantum method of the inverse problem and the Heisenberg X Y Z model
-
English transl., L. A. Takhtadzhan and L. D. Faddeev, "The quantum method of the inverse problem and the Heisenberg X Y Z model", Russian Math. Surveys 34:5 (1979), 11-68.
-
(1979)
Russian Math. Surveys
, vol.34
, Issue.5
, pp. 11-68
-
-
English transl, L.1
Takhtadzhan, A.2
Faddeev, L.D.3
-
6
-
-
0011630061
-
Partition function of the eight-vertex lattice model
-
R. J. Baxter, "Partition function of the eight-vertex lattice model", Ann. Physics 70:1 (1972), 193-228.
-
(1972)
Ann. Physics
, vol.70
, Issue.1
, pp. 193-228
-
-
Baxter, R.J.1
-
7
-
-
85164648650
-
-
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, Conformal field theory and solvable lattice models (Kyoto, 1986), Adv. Stud. Pure Math., 16, Academic Press, Boston, MA 1988, pp. 17-122.
-
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", Conformal field theory and solvable lattice models (Kyoto, 1986), Adv. Stud. Pure Math., vol. 16, Academic Press, Boston, MA 1988, pp. 17-122.
-
-
-
-
8
-
-
0001432807
-
Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions
-
Birkhäuser, Boston, MA
-
I. B. Frenkel and V. G. Turaev, "Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions", The Arnold-Gelfand mathematical seminars, Birkhäuser, Boston, MA 1997, pp. 171-204.
-
(1997)
The Arnold-Gelfand mathematical seminars
, pp. 171-204
-
-
Frenkel, I.B.1
Turaev, V.G.2
-
9
-
-
0034349855
-
Spectral transformation chains and some new biorthogonal rational functions
-
V. P. Spiridonov and A. S. Zhedanov, "Spectral transformation chains and some new biorthogonal rational functions", Comm. Math. Phys. 210:1 (2000), 49-83.
-
(2000)
Comm. Math. Phys
, vol.210
, Issue.1
, pp. 49-83
-
-
Spiridonov, V.P.1
Zhedanov, A.S.2
-
10
-
-
85164637270
-
-
V. P. Spiridonov, Theta hypergeometric series, Asymptotic combinatorics with application to mathematical physics (St. Petersburg, 2001), NATO Sci. Ser. II Math. Phys. Chem., 77, Kluwer, Dordrecht 2002, pp. 307-327; arXiv: math/0303204.
-
V. P. Spiridonov, "Theta hypergeometric series", Asymptotic combinatorics with application to mathematical physics (St. Petersburg, 2001), NATO Sci. Ser. II Math. Phys. Chem., vol. 77, Kluwer, Dordrecht 2002, pp. 307-327; arXiv: math/0303204.
-
-
-
-
11
-
-
85164650044
-
-
V. P. Spiridonov, Theta hypergeometric integrals,15:6 (2003), 161-215; Reprint, V. P. Spiridonov, Theta hypergeometric integrals, St. Petersburg Math. J. 15:6 (2004), 929-967; arXiv: math/0303205.
-
V. P. Spiridonov, "Theta hypergeometric integrals",15:6 (2003), 161-215; Reprint, V. P. Spiridonov, "Theta hypergeometric integrals", St. Petersburg Math. J. 15:6 (2004), 929-967; arXiv: math/0303205.
-
-
-
-
12
-
-
0003864328
-
-
McGraw-Hill, New York-Toronto-London
-
A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher transcendental functions, vol. I, McGraw-Hill, New York-Toronto-London 1953.
-
(1953)
Higher transcendental functions
, vol.1
-
-
Erdélyi, A.1
Magnus, W.2
Oberhettinger, F.3
Tricomi, F.G.4
-
13
-
-
0000457764
-
On the theory of the multiple gamma function
-
E. W. Barnes, "On the theory of the multiple gamma function", Cambridge Trans. 19 (1904), 374-425.
-
(1904)
Cambridge Trans
, vol.19
, pp. 374-425
-
-
Barnes, E.W.1
-
14
-
-
0001280742
-
The basic gamma-function and the elliptic functions
-
F. H. Jackson, "The basic gamma-function and the elliptic functions", Proc. Roy. Soc. London Ser. A 76:508 (1905), 127-144.
-
(1905)
Proc. Roy. Soc. London Ser. A
, vol.76
, Issue.508
, pp. 127-144
-
-
Jackson, F.H.1
-
15
-
-
0000404523
-
On a Kronecker limit formula for real quadratic field
-
T. Shintani, "On a Kronecker limit formula for real quadratic field", J. Fac. Sci. Univ. Tokyo Sect. IA Math. 24:1 (1977), 167-199.
-
(1977)
J. Fac. Sci. Univ. Tokyo Sect. IA Math
, vol.24
, Issue.1
, pp. 167-199
-
-
Shintani, T.1
-
16
-
-
0002340546
-
Multiple sine functions and Selberg zeta functions
-
N. Kurokawa, "Multiple sine functions and Selberg zeta functions", Proc. Japan Acad. Ser. A Math. Sci. 67:3 (1991), 61-64.
-
(1991)
Proc. Japan Acad. Ser. A Math. Sci
, vol.67
, Issue.3
, pp. 61-64
-
-
Kurokawa, N.1
-
17
-
-
0000780056
-
Discrete Heisenberg-Weyl group and modular group
-
L. D. Faddeev, "Discrete Heisenberg-Weyl group and modular group", Lett. Math. Phys. 34:3 (1995), 249-254.
-
(1995)
Lett. Math. Phys
, vol.34
, Issue.3
, pp. 249-254
-
-
Faddeev, L.D.1
-
18
-
-
0031540338
-
First order analytic difference equations and integrable quantum systems
-
S. N. M. Ruijsenaars, "First order analytic difference equations and integrable quantum systems", J. Math. Phys. 38:2 (1997), 1069-1146.
-
(1997)
J. Math. Phys
, vol.38
, Issue.2
, pp. 1069-1146
-
-
Ruijsenaars, S.N.M.1
-
19
-
-
85164649468
-
-
M. Jimbo and T. Miwa, Quantum KZ equation with |q| = 1 and correlation functions of the X X Z model in the gapless regime, J. Phys. A 29:12 (1996), 2923-2958.
-
M. Jimbo and T. Miwa, "Quantum KZ equation with |q| = 1 and correlation functions of the X X Z model in the gapless regime", J. Phys. A 29:12 (1996), 2923-2958.
-
-
-
-
20
-
-
0003192021
-
Geometry of g-hypergeometric functions, quantum affine algebras and elliptic quantum groups
-
arXiv: q-alg/9703044
-
V. Tarasov and A. Varchenko, "Geometry of g-hypergeometric functions, quantum affine algebras and elliptic quantum groups", Astérisque, 1997, no. 246, 1-135; arXiv: q-alg/9703044, 1997.
-
(1997)
Astérisque, 1997
, Issue.246
, pp. 1-135
-
-
Tarasov, V.1
Varchenko, A.2
-
21
-
-
0000561791
-
Strongly coupled quantum discrete Liouville theory. I: Algebraic approach and duality
-
L. D. Faddeev, R. M. Kashaev, and A. Yu. Volkov, "Strongly coupled quantum discrete Liouville theory. I: Algebraic approach and duality", Comm. Math. Phys. 219:1 (2001), 199-219.
-
(2001)
Comm. Math. Phys
, vol.219
, Issue.1
, pp. 199-219
-
-
Faddeev, L.D.1
Kashaev, R.M.2
Volkov, A.Y.3
-
23
-
-
2442630408
-
q(sl(2,ℝ)), the modular double and the multiparticle q-deformed Toda chains
-
q(sl(2,ℝ)), the modular double and the multiparticle q-deformed Toda chains", Comm. Math. Phys. 225:3 (2002), 573-609.
-
(2002)
Comm. Math. Phys
, vol.225
, Issue.3
, pp. 573-609
-
-
Kharchev, S.1
Lebedev, D.2
Semenov-Tian-Shansky, M.3
-
24
-
-
22544469184
-
Noncommutative hypergeometry
-
A. Yu. Volkov, "Noncommutative hypergeometry", Comm. Math. Phys. 258:2 (2005), 257-273.
-
(2005)
Comm. Math. Phys
, vol.258
, Issue.2
, pp. 257-273
-
-
Volkov, A.Y.1
-
26
-
-
4043167810
-
Shintani-Barnes zeta and gamma functions
-
E. Friedman and S. Ruijsenaars, "Shintani-Barnes zeta and gamma functions", Adv. Math. 187:2 (2004), 362-395.
-
(2004)
Adv. Math
, vol.187
, Issue.2
, pp. 362-395
-
-
Friedman, E.1
Ruijsenaars, S.2
-
27
-
-
8344258292
-
The modular properties and the integral representations of the multiple elliptic gamma functions
-
A. Narukawa, "The modular properties and the integral representations of the multiple elliptic gamma functions", Adv. Math. 189:2 (2004), 247-267.
-
(2004)
Adv. Math
, vol.189
, Issue.2
, pp. 247-267
-
-
Narukawa, A.1
-
28
-
-
85164648864
-
-
E. M. Rains, Limits of elliptic hypergeometric integrals, Ramanujan J. (to appear); arXiv: math/0607093, 2006.
-
E. M. Rains, "Limits of elliptic hypergeometric integrals", Ramanujan J. (to appear); arXiv: math/0607093, 2006.
-
-
-
-
30
-
-
3843098255
-
A Bailey tree for integrals
-
English transl., V. P. Spiridonov, "A Bailey tree for integrals", Theoret, and Math. Phys. 139:1 (2004), 536-541.
-
(2004)
Theoret, and Math. Phys
, vol.139
, Issue.1
, pp. 536-541
-
-
English transl, V.1
Spiridonov, P.2
-
31
-
-
29244432436
-
-
D. Sc. dissertation, Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna
-
V. P. Spiridonov, Elliptic hypergeometric functions, D. Sc. dissertation, Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 2004.
-
(2004)
Elliptic hypergeometric functions
-
-
Spiridonov, V.P.1
-
32
-
-
0034348688
-
An elliptic Macdonald-Morris conjecture and multiple modular hypergeometric sums
-
J. F. van Diejen and V. P. Spiridonov, "An elliptic Macdonald-Morris conjecture and multiple modular hypergeometric sums", Math. Res. Lett. 7:5-6 (2000), 729-746.
-
(2000)
Math. Res. Lett
, vol.7
, Issue.5-6
, pp. 729-746
-
-
van Diejen, J.F.1
Spiridonov, V.P.2
-
34
-
-
70350618906
-
Transformations of elliptic hypergeometric integrals
-
to appear, arXiv, math/0309252
-
E. M. Rains, "Transformations of elliptic hypergeometric integrals", Ann. of Math, (to appear); arXiv : math/0309252, 2003.
-
(2003)
Ann. of Math
-
-
Rains, E.M.1
-
35
-
-
33750306780
-
n-symmetric Abelian functions
-
n-symmetric Abelian functions", Duke Math. J. 135:1 (2006), 99-180.
-
(2006)
Duke Math. J
, vol.135
, Issue.1
, pp. 99-180
-
-
Rains, E.M.1
-
36
-
-
33748688802
-
Inversions of integral operators and elliptic beta integrals on root systems
-
V. P. Spiridonov and S. O. Warnaar, "Inversions of integral operators and elliptic beta integrals on root systems", Adv. Math. 207:1 (2006), 91-132.
-
(2006)
Adv. Math
, vol.207
, Issue.1
, pp. 91-132
-
-
Spiridonov, V.P.1
Warnaar, S.O.2
-
37
-
-
0034357401
-
On Barnes' multiple zeta and gamma functions
-
S. N. M. Ruijsenaars, "On Barnes' multiple zeta and gamma functions", Adv. Math. 156:1 (2000), 107-132.
-
(2000)
Adv. Math
, vol.156
, Issue.1
, pp. 107-132
-
-
Ruijsenaars, S.N.M.1
-
38
-
-
29244458380
-
Unit circle elliptic beta integrals
-
J. F. van Diejen and V. P. Spiridonov, "Unit circle elliptic beta integrals", Ramanujan J. 10:2 (2005), 187-204.
-
(2005)
Ramanujan J
, vol.10
, Issue.2
, pp. 187-204
-
-
van Diejen, J.F.1
Spiridonov, V.P.2
-
39
-
-
0000946162
-
9 rational functions
-
9 rational functions", Canad. J. Math. 38:3 (1986), 605-618.
-
(1986)
Canad. J. Math
, vol.38
, Issue.3
, pp. 605-618
-
-
Rahman, M.1
-
40
-
-
0001360108
-
Projection formulas, a reproducing kernel and a generating function for q-Wilson polynomials
-
B. Nassrallah and M. Rahman, "Projection formulas, a reproducing kernel and a generating function for q-Wilson polynomials", SIAM J. Math. Anal. 16:1 (1985), 186-197.
-
(1985)
SIAM J. Math. Anal
, vol.16
, Issue.1
, pp. 186-197
-
-
Nassrallah, B.1
Rahman, M.2
-
41
-
-
0001308382
-
Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
-
R. Askey and J. Wilson, "Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials", Mem. Amer. Math. Soc. 54:319 (1985).
-
(1985)
Mem. Amer. Math. Soc
, vol.54
, pp. 319
-
-
Askey, R.1
Wilson, J.2
-
42
-
-
0012747485
-
Beta integrals in Ramanujan's papers, his unpublished work and further examples
-
Urbana-Champaign, IL, Academic Press, Boston, MA
-
R. Askey, "Beta integrals in Ramanujan's papers, his unpublished work and further examples", Ramanujan revisited (Urbana-Champaign, IL, 1987), Academic Press, Boston, MA 1988, pp. 561-590.
-
(1987)
Ramanujan revisited
, pp. 561-590
-
-
Askey, R.1
-
43
-
-
85164634289
-
-
V. P. Spiridonov, Short proofs of the elliptic beta integrals, Ramanujan J. 13:1-3 (2007), 265-283; arXiv: math/0408369, 2004.
-
V. P. Spiridonov, "Short proofs of the elliptic beta integrals", Ramanujan J. 13:1-3 (2007), 265-283; arXiv: math/0408369, 2004.
-
-
-
-
44
-
-
0001169022
-
An algorithmic proof theory for hypergeometric (ordinary and "q") multisum/integral identities
-
H. S. Wilf and D. Zeilberger, "An algorithmic proof theory for hypergeometric (ordinary and "q") multisum/integral identities", Invent. Math. 108:3 (1992), 575-633.
-
(1992)
Invent. Math
, vol.108
, Issue.3
, pp. 575-633
-
-
Wilf, H.S.1
Zeilberger, D.2
-
45
-
-
85164655956
-
-
H. Rosengren, A proof of a multivariable elliptic summation formula conjectured by Warnaar, q-series with applications to combinatorics, number theory, and physics (Urbana, IL, 2000), Contemp. Math., 291, Amer. Math. Soc., Providence, RI 2001, pp. 193-202; arXiv: math/0101073, 2001.
-
H. Rosengren, "A proof of a multivariable elliptic summation formula conjectured by Warnaar", q-series with applications to combinatorics, number theory, and physics (Urbana, IL, 2000), Contemp. Math., vol. 291, Amer. Math. Soc., Providence, RI 2001, pp. 193-202; arXiv: math/0101073, 2001.
-
-
-
-
47
-
-
33846828437
-
Elliptic enumeration of nonintersecting lattice paths
-
M. Schlosser, "Elliptic enumeration of nonintersecting lattice paths", J. Combin. Theory Ser. A 114:3 (2007), 505-521.
-
(2007)
J. Combin. Theory Ser. A
, vol.114
, Issue.3
, pp. 505-521
-
-
Schlosser, M.1
-
49
-
-
85164640082
-
Abel's method on summation by parts and theta hypergeometric series
-
to appear
-
W. Chu and C. Jia, "Abel's method on summation by parts and theta hypergeometric series", J. Combin. Theory Ser. A (to appear).
-
J. Combin. Theory Ser. A
-
-
Chu, W.1
Jia, C.2
-
50
-
-
6444239366
-
Hyperbolic beta integrals
-
J. V. Stokman, "Hyperbolic beta integrals", Adv. Math. 190:1 (2005), 119-160.
-
(2005)
Adv. Math
, vol.190
, Issue.1
, pp. 119-160
-
-
Stokman, J.V.1
-
52
-
-
0036039842
-
An elliptic incarnation of the Bailey chain
-
V. P. Spiridonov, "An elliptic incarnation of the Bailey chain", Int. Math. Res. Not., 2002, no. 37, 1945-1977.
-
(2002)
Int. Math. Res. Not
, Issue.37
, pp. 1945-1977
-
-
Spiridonov, V.P.1
-
53
-
-
0035982986
-
Summation and transformation formulas for elliptic hypergeometric series
-
S.O. Warnaar, "Summation and transformation formulas for elliptic hypergeometric series", Constr. Approx. 18:4 (2002), 479-502.
-
(2002)
Constr. Approx
, vol.18
, Issue.4
, pp. 479-502
-
-
Warnaar, S.O.1
-
54
-
-
13544255722
-
Summation formulae for elliptic hypergeometric series
-
S.O. Warnaar, "Summation formulae for elliptic hypergeometric series", Proc. Amer. Math. Soc. 133:2 (2005), 519-527.
-
(2005)
Proc. Amer. Math. Soc
, vol.133
, Issue.2
, pp. 519-527
-
-
Warnaar, S.O.1
-
55
-
-
33751013958
-
Summation, transformation, and expansion formulas for multibasic theta hypergeometric series
-
arXiv: math/0505215
-
G. Gasper and M. Schlosser, "Summation, transformation, and expansion formulas for multibasic theta hypergeometric series", Adv. Stud. Contemp. Math. (Kyungshang) 11:1 (2005), 67-84; arXiv: math/0505215, 2005.
-
(2005)
Adv. Stud. Contemp. Math. (Kyungshang)
, vol.11
-
-
Gasper, G.1
Schlosser, M.2
-
56
-
-
14844343264
-
On Warnaar's elliptic matrix inversion and Karlsson-Minton-type elliptic hypergeometric series
-
H. Rosengren and M. Schlosser, "On Warnaar's elliptic matrix inversion and Karlsson-Minton-type elliptic hypergeometric series", J. Comput. Appl. Math. 178:1-2 (2005), 377-391.
-
(2005)
J. Comput. Appl. Math
, vol.178
, Issue.1-2
, pp. 377-391
-
-
Rosengren, H.1
Schlosser, M.2
-
58
-
-
33847195076
-
Elliptic hypergeometric functions and Calogero-Sutherland-type models
-
English transl., V. P. Spiridonov, "Elliptic hypergeometric functions and Calogero-Sutherland-type models", Theoret. Math. Phys. 150:2 (2007), 266-277.
-
(2007)
Theoret. Math. Phys
, vol.150
, Issue.2
, pp. 266-277
-
-
English transl, V.1
Spiridonov, P.2
-
60
-
-
0033517395
-
Generalized hypergeometric function satisfying four analytic difference equations of Askey-Wilson type
-
S. N. M. Ruijsenaars, "Generalized hypergeometric function satisfying four analytic difference equations of Askey-Wilson type", Comm. Math. Phys. 206:3 (1999), 639-690.
-
(1999)
Comm. Math. Phys
, vol.206
, Issue.3
, pp. 639-690
-
-
Ruijsenaars, S.N.M.1
-
61
-
-
34547843623
-
Properties of generalized univariate hypergeometric functions
-
1 2007, arXiv: math/0607250
-
F. J. van de Bult, E. M. Rains, and J. V. Stokman, "Properties of generalized univariate hypergeometric functions", Comm. Math. Phys. 275:1 (2007), 37-95; arXiv: math/0607250, 2006.
-
(2006)
Comm. Math. Phys
, vol.275
, pp. 37-95
-
-
van de Bult, F.J.1
Rains, E.M.2
Stokman, J.V.3
-
62
-
-
21344479784
-
Integrability of difference Calogero-Moser systems
-
J. F. van Diejen, "Integrability of difference Calogero-Moser systems", J. Math. Phys. 35:6 (1994), 2983-3004.
-
(1994)
J. Math. Phys
, vol.35
, Issue.6
, pp. 2983-3004
-
-
van Diejen, J.F.1
-
63
-
-
0031582460
-
Quantum integrability of the generalized elliptic Ruijsenaars models
-
Y. Komori and K. Hikami, "Quantum integrability of the generalized elliptic Ruijsenaars models", J. Phys. A 30:12 (1997), 4341-4364.
-
(1997)
J. Phys. A
, vol.30
, Issue.12
, pp. 4341-4364
-
-
Komori, Y.1
Hikami, K.2
-
64
-
-
3543099119
-
Complete integrability of relativistic Calogero-Moser systems and elliptic function identities
-
S. N. M. Ruijsenaars, "Complete integrability of relativistic Calogero-Moser systems and elliptic function identities", Comm. Math. Phys. 110:2 (1987), 191-213.
-
(1987)
Comm. Math. Phys
, vol.110
, Issue.2
, pp. 191-213
-
-
Ruijsenaars, S.N.M.1
-
65
-
-
0001842633
-
Lax representation with spectral parameter on a torus for integrable particle systems
-
V. I. Inozemtsev, "Lax representation with spectral parameter on a torus for integrable particle systems", Lett. Math. Phys. 17:1 (1989), 11-17.
-
(1989)
Lett. Math. Phys
, vol.17
, Issue.1
, pp. 11-17
-
-
Inozemtsev, V.I.1
-
66
-
-
85164648679
-
-
G. E. Andrews, Bailey's transform, lemma, chains and tree, Special functions 2000: current perspective and future directions (Tempe, AZ), NATO Sci. Ser. II Math. Phys. Chem., 30, Kluwer, Dordrecht 2001, pp. 1-22.
-
G. E. Andrews, "Bailey's transform, lemma, chains and tree", Special functions 2000: current perspective and future directions (Tempe, AZ), NATO Sci. Ser. II Math. Phys. Chem., vol. 30, Kluwer, Dordrecht 2001, pp. 1-22.
-
-
-
-
67
-
-
1042303120
-
Extensions of the well-poised and elliptic well-poised Bailey lemma
-
S. O. Warnaar, "Extensions of the well-poised and elliptic well-poised Bailey lemma", Indag. Math. (N.S.) 14:3-4 (2003), 571-588.
-
(2003)
Indag. Math. (N.S.)
, vol.14
, Issue.3-4
, pp. 571-588
-
-
Warnaar, S.O.1
-
68
-
-
0000863755
-
A matrix inverse
-
D. M. Bressoud, "A matrix inverse", Proc. Amer. Math. Soc. 88:3 (1983), 446-448.
-
(1983)
Proc. Amer. Math. Soc
, vol.88
, Issue.3
, pp. 446-448
-
-
Bressoud, D.M.1
-
69
-
-
27844563079
-
An extension of Warnaar's matrix inversion
-
X. R. Ma, "An extension of Warnaar's matrix inversion", Proc. Amer. Math. Soc. 133:11 (2005), 3179-3189.
-
(2005)
Proc. Amer. Math. Soc
, vol.133
, Issue.11
, pp. 3179-3189
-
-
Ma, X.R.1
-
70
-
-
0033474021
-
Biorthogonal rational functions and the generalized eigenvalue problem
-
A. Zhedanov, "Biorthogonal rational functions and the generalized eigenvalue problem", J. Approx. Theory 101:2 (1999), 303-329.
-
(1999)
J. Approx. Theory
, vol.101
, Issue.2
, pp. 303-329
-
-
Zhedanov, A.1
-
71
-
-
0141820548
-
Generalized orthogonality and continued fractions
-
M. E. H. Ismail and D. R. Masson, "Generalized orthogonality and continued fractions", J. Approx. Theory 83:1 (1995), 1-40.
-
(1995)
J. Approx. Theory
, vol.83
, Issue.1
, pp. 1-40
-
-
Ismail, M.E.H.1
Masson, D.R.2
-
72
-
-
85164655259
-
-
English transl., A.A. Gonchar, On the speed of rational approximation of some analytic functions, Math. USSR-Sb. 34:2 (1978), 131-145.
-
English transl., A.A. Gonchar, "On the speed of rational approximation of some analytic functions", Math. USSR-Sb. 34:2 (1978), 131-145.
-
-
-
-
73
-
-
33645338835
-
On Markov's theorem for multipoint Padé approximants
-
English transl., A. A. Gonchar and G. López Lagomasino, "On Markov's theorem for multipoint Padé approximants", Math. USSR-Sb. 34:4 (1978), 449-459.
-
(1978)
Math. USSR-Sb
, vol.34
, Issue.4
, pp. 449-459
-
-
English transl, A.1
Gonchar, A.2
López Lagomasino, G.3
-
74
-
-
0003153325
-
Classical biorthogonal rational functions on elliptic grids
-
V. P. Spiridonov and A. S. Zhedanov, "Classical biorthogonal rational functions on elliptic grids", C. R. Math. Acad. Sci. Soc. R. Can. 22:2 (2000), 70-76.
-
(2000)
C. R. Math. Acad. Sci. Soc. R. Can
, vol.22
, Issue.2
, pp. 70-76
-
-
Spiridonov, V.P.1
Zhedanov, A.S.2
-
75
-
-
0000102490
-
Orthogonal functions from Gram determinants
-
J. A. Wilson, "Orthogonal functions from Gram determinants", SIAM J. Math. Anal. 22:4 (1991), 1147-1155.
-
(1991)
SIAM J. Math. Anal
, vol.22
, Issue.4
, pp. 1147-1155
-
-
Wilson, J.A.1
-
76
-
-
33845728851
-
An elementary approach to 6j-symbols (classical, quantum, rational, trigonometric, and elliptic)
-
H. Rosengren, "An elementary approach to 6j-symbols (classical, quantum, rational, trigonometric, and elliptic)", Ramanujan J. 13:1-3 (2007), 131-166.
-
(2007)
Ramanujan J
, vol.13
, Issue.131-166
, pp. 1-3
-
-
Rosengren, H.1
-
77
-
-
21944434494
-
Contiguous relations, continued fractions and orthogonality
-
D. P. Gupta and D. R. Masson, "Contiguous relations, continued fractions and orthogonality", Trans. Amer. Math. Soc. 350:2 (1998), 769-808.
-
(1998)
Trans. Amer. Math. Soc
, vol.350
, Issue.2
, pp. 769-808
-
-
Gupta, D.P.1
Masson, D.R.2
-
78
-
-
21344496500
-
Watson's basic analogue of Ramanujan's entry 40 and its generalization
-
D. P. Gupta and D. R. Masson, "Watson's basic analogue of Ramanujan's entry 40 and its generalization", SIAM J. Math. Anal. 25:2 (1994), 429-440.
-
(1994)
SIAM J. Math. Anal
, vol.25
, Issue.2
, pp. 429-440
-
-
Gupta, D.P.1
Masson, D.R.2
-
79
-
-
85164655414
-
-
V. P. Spiridonov, Continuous biorthogonality of an elliptic hypergeometric function, St. Petersburg Math. J. (to appear)]; arXiv: 0801.4137, 2008.
-
V. P. Spiridonov, "Continuous biorthogonality of an elliptic hypergeometric function", St. Petersburg Math. J. (to appear)]; arXiv: 0801.4137, 2008.
-
-
-
-
80
-
-
10244260540
-
Sklyanin invariant integration
-
arXiv: math/0405072
-
H. Rosengren, "Sklyanin invariant integration", Int. Math. Res. Not., 2004, no. 60, 3207-3232; arXiv: math/0405072, 2004.
-
(2004)
Int. Math. Res. Not
, Issue.60
, pp. 3207-3232
-
-
Rosengren, H.1
-
81
-
-
34250143502
-
Some algebraic structures connected with the Yang-Baxter equation
-
English transl., E. K. Sklyanin, "Some algebraic structures connected with the Yang-Baxter equation", Funct. Anal. Appl. 16:4 (1982), 263-270.
-
(1982)
Funct. Anal. Appl
, vol.16
, Issue.4
, pp. 263-270
-
-
English transl, E.1
Sklyanin, K.2
-
82
-
-
0040694601
-
Some algebraic structures connected with the Yang-Baxter equation. Representations of quantum algebras
-
English transl., E. K. Sklyanin, "Some algebraic structures connected with the Yang-Baxter equation. Representations of quantum algebras", Funct. Anal. Appl. 17:4 (1983), 273-284.
-
(1983)
Funct. Anal. Appl
, vol.17
, Issue.4
, pp. 273-284
-
-
English transl, E.1
Sklyanin, K.2
-
83
-
-
85164637435
-
-
2, Geometry of differential equations, Amer. Math. Soc. Transl. Ser. 2, 186, Amer. Math. Soc., Providence, RI 1998, pp. 131-151.
-
2", Geometry of differential equations, Amer. Math. Soc. Transl. Ser. 2, vol. 186, Amer. Math. Soc., Providence, RI 1998, pp. 131-151.
-
-
-
-
84
-
-
0038345715
-
Modular double of a quantum group
-
Dijon, Math. Phys. Stud, 21, Kluwer, Dordrecht
-
L. D. Faddeev, "Modular double of a quantum group", Conférence Moshé Flato (Dijon, 1999), vol. I, Math. Phys. Stud., vol. 21, Kluwer, Dordrecht 2000, pp. 149-156.
-
(1999)
Conférence Moshé Flato
, vol.1
, pp. 149-156
-
-
Faddeev, L.D.1
-
86
-
-
0346499268
-
Elliptic hypergeometric series on root systems
-
H. Rosengren, "Elliptic hypergeometric series on root systems", Adv. Math. 181:2 (2004), 417-447.
-
(2004)
Adv. Math
, vol.181
, Issue.2
, pp. 417-447
-
-
Rosengren, H.1
-
87
-
-
0000211724
-
Multilateral summation theorems for ordinary and basic hypergeometric series in U(n)
-
R. A. Gustafson, "Multilateral summation theorems for ordinary and basic hypergeometric series in U(n)", SIAM J. Math. Anal. 18:6 (1987), 1576-1596.
-
(1987)
SIAM J. Math. Anal
, vol.18
, Issue.6
, pp. 1576-1596
-
-
Gustafson, R.A.1
-
88
-
-
0003321117
-
The major counting of nonintersecting lattice paths and generating functions for tableaux
-
C. Krattenthaler, "The major counting of nonintersecting lattice paths and generating functions for tableaux", Mem. Amer. Math. Soc. 115:552 (1995).
-
(1995)
Mem. Amer. Math. Soc
, vol.115
, pp. 552
-
-
Krattenthaler, C.1
-
89
-
-
1042279873
-
Multiple elliptic hypergeometric series. An approach from the Cauchy determinant
-
Y. Kajihara and M. Noumi, "Multiple elliptic hypergeometric series. An approach from the Cauchy determinant", Indag. Math. (N.S.) 14:3-4 (2003), 395-421.
-
(2003)
Indag. Math. (N.S.)
, vol.14
, Issue.3-4
, pp. 395-421
-
-
Kajihara, Y.1
Noumi, M.2
-
90
-
-
1042291519
-
Summations and transformations for multiple basic and elliptic hypergeometric series by determinant evaluations
-
H. Rosengren and M. Schlosser, "Summations and transformations for multiple basic and elliptic hypergeometric series by determinant evaluations", Indag. Math. (N.S.) 14:3-4 (2003), 483-513.
-
(2003)
Indag. Math. (N.S.)
, vol.14
, Issue.3-4
, pp. 483-513
-
-
Rosengren, H.1
Schlosser, M.2
-
91
-
-
33750616917
-
Recurrences for elliptic hypergeometric integrals
-
arXiv: math/0504285
-
E. M. Rains, "Recurrences for elliptic hypergeometric integrals", Rokko Lect. Math. 18 (2005), 183-199; arXiv: math/0504285, 2005.
-
(2005)
Rokko Lect. Math
, vol.18
, pp. 183-199
-
-
Rains, E.M.1
-
92
-
-
33845302952
-
Elliptic determinant evaluations and the Macdonald identities for affine root systems
-
H. Rosengren and M. Schlosser, "Elliptic determinant evaluations and the Macdonald identities for affine root systems", Compos. Math. 142:4 (2006), 937-961.
-
(2006)
Compos. Math
, vol.142
, Issue.4
, pp. 937-961
-
-
Rosengren, H.1
Schlosser, M.2
-
93
-
-
33750627763
-
Sums of triangular numbers from the Frobenius determinant
-
H. Rosengren, "Sums of triangular numbers from the Frobenius determinant", Adv. Math. 208:2 (2007), 935-961.
-
(2007)
Adv. Math
, vol.208
, Issue.2
, pp. 935-961
-
-
Rosengren, H.1
-
95
-
-
0001086420
-
Some q-beta and Mellin-Barnes integrals with many parameters associated to the classical groups
-
R. A. Gustafson, "Some q-beta and Mellin-Barnes integrals with many parameters associated to the classical groups", SIAM J. Math. Anal. 23:2 (1992), 525-551.
-
(1992)
SIAM J. Math. Anal
, vol.23
, Issue.2
, pp. 525-551
-
-
Gustafson, R.A.1
-
96
-
-
3843137762
-
Some q-beta integrals on SU(n) and Sp(n) that generalize the Askey-Wilson and Nassrallah-Rahman integrals
-
R. A. Gustafson, "Some q-beta integrals on SU(n) and Sp(n) that generalize the Askey-Wilson and Nassrallah-Rahman integrals", SIAM J. Math. Anal. 25:2 (1994), 441-449.
-
(1994)
SIAM J. Math. Anal
, vol.25
, Issue.2
, pp. 441-449
-
-
Gustafson, R.A.1
-
97
-
-
85164651843
-
-
P. J. Forrester and S. O. Warnaar, The importance of the Selberg integral, Bull. Amer. Math. Soc. (N.S.) (to appear); arXiv: 0710.3981, 2007.
-
P. J. Forrester and S. O. Warnaar, "The importance of the Selberg integral", Bull. Amer. Math. Soc. (N.S.) (to appear); arXiv: 0710.3981, 2007.
-
-
-
-
98
-
-
85164656861
-
-
I. G. Macdonald, Constant term identities, orthogonal polynomials, and affine Hecke algebras, Proceedings of the International Congress of Mathematicians, I (Berlin, 1998), Doc. Math., 1998, 303-317.
-
I. G. Macdonald, "Constant term identities, orthogonal polynomials, and affine Hecke algebras", Proceedings of the International Congress of Mathematicians, vol. I (Berlin, 1998), Doc. Math., 1998, 303-317.
-
-
-
-
99
-
-
0006751312
-
A short proof of Selberg's generalized beta formula
-
G. W. Anderson, "A short proof of Selberg's generalized beta formula", Forum Math. 3:4 (1991), 415-417.
-
(1991)
Forum Math
, vol.3
, Issue.4
, pp. 415-417
-
-
Anderson, G.W.1
-
101
-
-
0001700934
-
Modular hypergeometric residue sums of elliptic Selberg integrals
-
J. F. van Diejen and V. P. Spiridonov, "Modular hypergeometric residue sums of elliptic Selberg integrals", Lett. Math. Phys. 58:3 (2001), 223-238.
-
(2001)
Lett. Math. Phys
, vol.58
, Issue.3
, pp. 223-238
-
-
van Diejen, J.F.1
Spiridonov, V.P.2
-
102
-
-
85164649217
-
-
n, Jack, Hall-Littlewood and Macdonald polynomials, Contemp. Math., 417, Amer. Math. Soc., Providence, RI 2006, pp. 127-155.
-
n", Jack, Hall-Littlewood and Macdonald polynomials, Contemp. Math., vol. 417, Amer. Math. Soc., Providence, RI 2006, pp. 127-155.
-
-
-
-
103
-
-
0001625649
-
An SU(n) q-beta integral transformation and multiple hypergeometric series identities
-
R. Y. Denis and R. A. Gustafson, "An SU(n) q-beta integral transformation and multiple hypergeometric series identities", SIAM J. Math. Anal. 23:2 (1992), 552-561.
-
(1992)
SIAM J. Math. Anal
, vol.23
, Issue.2
, pp. 552-561
-
-
Denis, R.Y.1
Gustafson, R.A.2
-
104
-
-
0002912280
-
Multiple q-series and U(n) generalizations of Ramanujan's ψ sum
-
Urbana-Champaign, IL, Academic Press, Boston, MA
-
S. C. Milne, "Multiple q-series and U(n) generalizations of Ramanujan's ψ sum", Ramanujan revisited (Urbana-Champaign, IL, 1987), Academic Press, Boston, MA 1988, pp. 473-524.
-
(1987)
Ramanujan revisited
, pp. 473-524
-
-
Milne, S.C.1
-
105
-
-
0040743762
-
Generalisations of Legendre's formula KE′ -(K- E)K′ = 1/2π
-
A. L. Dixon, "Generalisations of Legendre's formula KE′ -(K- E)K′ = 1/2π", Proc. London Math. Soc. 2:1 (1905), 206-224.
-
(1905)
Proc. London Math. Soc
, vol.2
, Issue.1
, pp. 206-224
-
-
Dixon, A.L.1
-
106
-
-
33845794288
-
Elliptic grids, rational functions, and the Pade interpolation
-
V. P. Spiridonov and A. S. Zhedanov, "Elliptic grids, rational functions, and the Pade interpolation", Ramanujan J. 13:1-3 (2007), 285-310.
-
(2007)
Ramanujan J
, vol.13
, Issue.1-3
, pp. 285-310
-
-
Spiridonov, V.P.1
Zhedanov, A.S.2
-
107
-
-
57049151983
-
Padé interpolation table and biorthogonal rational functions
-
A. Zhedanov, "Padé interpolation table and biorthogonal rational functions", Rokko Lect. Math. 18 (2005), 323-363.
-
(2005)
Rokko Lect. Math
, vol.18
, pp. 323-363
-
-
Zhedanov, A.1
-
108
-
-
85164635012
-
-
T. H. Koornwinder, Askey-Wilaon polynomials for root systems of type BC, Hypergeometric functions on domains of positivity, Jack polynomials, and applications (Tampa, FL, 1991), Contemp. Math., 138, Amer. Math. Soc., Providence, RI 1992, pp. 189-204.
-
T. H. Koornwinder, "Askey-Wilaon polynomials for root systems of type BC", Hypergeometric functions on domains of positivity, Jack polynomials, and applications (Tampa, FL, 1991), Contemp. Math., vol. 138, Amer. Math. Soc., Providence, RI 1992, pp. 189-204.
-
-
-
-
109
-
-
0032390708
-
BC-type interpolation Macdonald polynomials and binomial formula for Koornwinder polynomials
-
A. Okounkov, "BC-type interpolation Macdonald polynomials and binomial formula for Koornwinder polynomials", Transform. Groups 3:2 (1998), 181-207.
-
(1998)
Transform. Groups
, vol.3
, Issue.2
, pp. 181-207
-
-
Okounkov, A.1
-
110
-
-
2942674899
-
Hypergeometric theta functions and elliptic Macdonald polynomials
-
G. Felder and A. Varchenko, "Hypergeometric theta functions and elliptic Macdonald polynomials", Int. Math. Res. Not., 2004, no. 21, 1037-1055.
-
(2004)
Int. Math. Res. Not
, Issue.21
, pp. 1037-1055
-
-
Felder, G.1
Varchenko, A.2
-
111
-
-
0035534919
-
Rational surfaces associated with affine root systems and geometry of the Painlevé equations
-
H. Sakai, "Rational surfaces associated with affine root systems and geometry of the Painlevé equations", Comm. Math. Phys. 220:1 (2001), 165-229.
-
(2001)
Comm. Math. Phys
, vol.220
, Issue.1
, pp. 165-229
-
-
Sakai, H.1
-
113
-
-
33748686566
-
Askey-Wilson type integrals associated with root systems
-
M. Ito, "Askey-Wilson type integrals associated with root systems", Ramanujan J. 12:1 (2006), 131-151.
-
(2006)
Ramanujan J
, vol.12
, Issue.1
, pp. 131-151
-
-
Ito, M.1
-
114
-
-
84907199085
-
The associated Askey-Wilson polynomials
-
M. E. H. Ismail and M. Rahman, "The associated Askey-Wilson polynomials", Trans. Amer. Math. Soc. 328:1 (1991), 201-237.
-
(1991)
Trans. Amer. Math. Soc
, vol.328
, Issue.1
, pp. 201-237
-
-
Ismail, M.E.H.1
Rahman, M.2
-
115
-
-
85164642804
-
-
V. P. Spiridonov, A multiparameter summation formula for Riemann theta functions, Jack, Hall-Littlewood and Macdonald polynomials, Contemp. Math., 417, Amer. Math. Soc., Providence, RI 2006, pp. 345-353.
-
V. P. Spiridonov, "A multiparameter summation formula for Riemann theta functions", Jack, Hall-Littlewood and Macdonald polynomials, Contemp. Math., vol. 417, Amer. Math. Soc., Providence, RI 2006, pp. 345-353.
-
-
-
-
116
-
-
23944434157
-
The vertex-face correspondence and the elliptic 6j-symbols
-
3 2005, arXiv: math/0603725
-
H. Konno, "The vertex-face correspondence and the elliptic 6j-symbols", Lett. Math. Phys. 72:3 (2005), 243-258; arXiv: math/0603725, 2005.
-
(2005)
Lett. Math. Phys
, vol.72
, pp. 243-258
-
-
Konno, H.1
-
117
-
-
85164654242
-
-
English transl., N.I. Akhiezer, Elements of the theory of elliptic functions, Transl. Math. Monogr., 79, Amer. Math. Soc., Providence, RI 1990.
-
English transl., N.I. Akhiezer, Elements of the theory of elliptic functions, Transl. Math. Monogr., vol. 79, Amer. Math. Soc., Providence, RI 1990.
-
-
-
-
118
-
-
0003957155
-
-
Progr. Math, Birkhäuser, Boston, MA
-
M. Eichler and D. Zagier, The theory of Jacobi forms, Progr. Math., vol. 55, Birkhäuser, Boston, MA 1985.
-
(1985)
The theory of Jacobi forms
, vol.55
-
-
Eichler, M.1
Zagier, D.2
|