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Volumn 18, Issue 4, 2002, Pages 479-502

Summation and transformation formulas for elliptic hypergeometric series

Author keywords

Elliptic functions; Elliptic hypergeometric series

Indexed keywords


EID: 0035982986     PISSN: 01764276     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00365-002-0501-6     Document Type: Article
Times cited : (110)

References (38)
  • 1
    • 0032376621 scopus 로고    scopus 로고
    • Determinants in plane partition enumeration
    • G. E. ANDREWS, D. W. STANTON (1998): Determinants in plane partition enumeration. European J. Combin., 19:273-282.
    • (1998) European J. Combin. , vol.19 , pp. 273-282
    • Andrews, G.E.1    Stanton, D.W.2
  • 2
    • 0001078490 scopus 로고
    • An identity involving Heine's basic hypergeometric series
    • W. N. BAILEY (1929): An identity involving Heine's basic hypergeometric series. J. London. Math. Soc., 4:254-257.
    • (1929) J. London. Math. Soc. , vol.4 , pp. 254-257
    • Bailey, W.N.1
  • 3
    • 49549172862 scopus 로고
    • Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain. II. Equivalence to a generalized ice-type model
    • R. J. BAXTER (1973): Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain. II. Equivalence to a generalized ice-type model. Ann. Physics, 76:25-47.
    • (1973) Ann. Physics , vol.76 , pp. 25-47
    • Baxter, R.J.1
  • 4
    • 0031572792 scopus 로고    scopus 로고
    • Generalized bibasic hypergeometric series and their U(n) extensions
    • G. BHATNAGAR, S. C. MILNE (1997): Generalized bibasic hypergeometric series and their U(n) extensions. Adv. in Math., 131:188-252.
    • (1997) Adv. in Math. , vol.131 , pp. 188-252
    • Bhatnagar, G.1    Milne, S.C.2
  • 6
    • 0003017557 scopus 로고
    • The Bailey lattice: An introduction
    • (G. E. Andrews et al., eds.). New York: Academic Press
    • D. M. BRESSOUD (1988): The Bailey lattice: An introduction. In: Ramanujan Revisited (G. E. Andrews et al., eds.). New York: Academic Press, pp. 57-67.
    • (1988) Ramanujan Revisited , pp. 57-67
    • Bressoud, D.M.1
  • 7
    • 0013006176 scopus 로고
    • Inversion techniques and combinatorial identities-Strange evaluations of basic hyper-geometric series
    • W. CHU (1994): Inversion techniques and combinatorial identities-Strange evaluations of basic hyper-geometric series. Compositio Math., 91:121-144.
    • (1994) Compositio Math. , vol.91 , pp. 121-144
    • Chu, W.1
  • 8
    • 0012908340 scopus 로고
    • Inversion techniques and combinatorial identities-Jackson's q-analogue of the Dougall-Dixon theorem and the dual formulae
    • W. CHU (1995): Inversion techniques and combinatorial identities-Jackson's q-analogue of the Dougall-Dixon theorem and the dual formulae. Compositio Math., 95:43-68.
    • (1995) Compositio Math. , vol.95 , pp. 43-68
    • Chu, W.1
  • 10
    • 0001625649 scopus 로고
    • An SU(n) q-beta integral transformation and multiple hyper-geometric series identities
    • R. Y. DENIS, R. A. GUSTAFSON (1992): An SU(n) q-beta integral transformation and multiple hyper-geometric series identities. SIAM J. Math. Anal., 23:552-561.
    • (1992) SIAM J. Math. Anal. , vol.23 , pp. 552-561
    • Denis, R.Y.1    Gustafson, R.A.2
  • 11
    • 21944450779 scopus 로고    scopus 로고
    • On certain multiple Bailey, Rogers and Dougall-type summation formulas
    • J. F. VAN DIEJEN (1997): On certain multiple Bailey, Rogers and Dougall-type summation formulas. Publ. Res. Inst. Math. Sci., 33:483-508.
    • (1997) Publ. Res. Inst. Math. Sci. , vol.33 , pp. 483-508
    • Van Diejen, J.F.1
  • 13
    • 0001432807 scopus 로고    scopus 로고
    • Elliptic solutions of the Yang-Baxter equation and modular hyper-geometric functions
    • Boston, MA: Birkhäuser
    • I. B. FRENKEL, V. G. TURAEV (1997): Elliptic solutions of the Yang-Baxter equation and modular hyper-geometric functions. The Arnold-Gelfand Mathematical Seminars. Boston, MA: Birkhäuser, pp. 171-204.
    • (1997) The Arnold-Gelfand Mathematical Seminars , pp. 171-204
    • Frenkel, I.B.1    Turaev, V.G.2
  • 14
    • 84966234176 scopus 로고
    • Summation, transformation, and expansion formulas for bibasic series
    • G. GASPER (1989): Summation, transformation, and expansion formulas for bibasic series. Trans. Amer. Math. Soc., 312:257-277.
    • (1989) Trans. Amer. Math. Soc. , vol.312 , pp. 257-277
    • Gasper, G.1
  • 16
    • 0002005655 scopus 로고
    • An indefinite bibasic summation formula and some quadratic, cubic and quartic summation and transformation formulas
    • G. GASPER, M. RAHMAN (1990): An indefinite bibasic summation formula and some quadratic, cubic and quartic summation and transformation formulas. Canad. J. Math., 42:1-27.
    • (1990) Canad. J. Math. , vol.42 , pp. 1-27
    • Gasper, G.1    Rahman, M.2
  • 17
    • 84967774617 scopus 로고
    • Applications of q-Lagrange inversion to basic hypergeometric series
    • I. GESSEL, D. STANTON (1983): Applications of q-Lagrange inversion to basic hypergeometric series. Trans. Amer. Math. Soc., 277:173-201.
    • (1983) Trans. Amer. Math. Soc. , vol.277 , pp. 173-201
    • Gessel, I.1    Stanton, D.2
  • 18
    • 0000740312 scopus 로고
    • Another family of q-Lagrange inversion formulas
    • I. GESSEL, D. STANTON (1986): Another family of q-Lagrange inversion formulas. Rocky Mountain J. Math., 16:373-384.
    • (1986) Rocky Mountain J. Math. , vol.16 , pp. 373-384
    • Gessel, I.1    Stanton, D.2
  • 19
    • 0013016828 scopus 로고    scopus 로고
    • 1-transformations
    • (M. E. H. Ismail et al. eds.). Fields Inst. Commun. Providence, RI: American Mathematical Society
    • 1-transformations. In: Special Functions, q-Series and Related Topics (M. E. H. Ismail et al. eds.). Fields Inst. Commun., Vol. 14. Providence, RI: American Mathematical Society, pp. 83-89.
    • (1997) Special Functions, q-Series and Related Topics , vol.14 , pp. 83-89
    • Gustafson, R.A.1    Krattenthaler, C.2
  • 20
    • 0001311498 scopus 로고
    • Summation of q-hypergeometric series
    • F. H. JACKSON (1921): Summation of q-hypergeometric series. Messenger Math., 50:101-112.
    • (1921) Messenger Math. , vol.50 , pp. 101-112
    • Jackson, F.H.1
  • 21
    • 0003321117 scopus 로고
    • The major counting of nonintersecting lattice paths and generating functions for tableaux
    • C. KRATTENTHALER (1995): The major counting of nonintersecting lattice paths and generating functions for tableaux. Mem. Amer. Math. Soc., 115:no. 552.
    • (1995) Mem. Amer. Math. Soc. , vol.115 , Issue.552
    • Krattenthaler, C.1
  • 23
    • 0001830930 scopus 로고    scopus 로고
    • Advanced determinant calculus
    • Art. B42q
    • C. KRATTENTHALER (1999): Advanced Determinant Calculus. Sém. Lothar. Combin., Vol. 42, Art. B42q, 41pp.
    • (1999) Sém. Lothar. Combin. , vol.42 , pp. 41
    • Krattenthaler, C.1
  • 25
    • 0002912280 scopus 로고
    • 1 sum
    • (G. E. Andrews et al. eds.). Boston, MA: Academic Press
    • 1 sum. In: Ramanujan Revisited (G. E. Andrews et al. eds.). Boston, MA: Academic Press, pp. 473-524.
    • (1988) Ramanujan Revisited , pp. 473-524
    • Milne, S.C.1
  • 26
    • 0000132675 scopus 로고
    • (1)
    • Theta Functions-Bowdoin 1987 (L. Ehrenpreis and R. C. Gunning, eds.). Providence, RI: American Mathematical Society
    • (1). In: Theta Functions-Bowdoin 1987 (L. Ehrenpreis and R. C. Gunning, eds.). Proc. Sympos. Pure Math., Vol. 49 (Part 2). Providence, RI: American Mathematical Society, pp. 323-359.
    • (1989) Proc. Sympos. Pure Math. , vol.49 , Issue.PART 2 , pp. 323-359
    • Milne, S.C.1
  • 27
    • 43949159722 scopus 로고
    • A q-analog of a Whipple's transformation for hypergeometric series in U(n)
    • S. C. MILNE (1994): A q-analog of a Whipple's transformation for hypergeometric series in U(n). Adv. in Math., 108:1-76.
    • (1994) Adv. in Math. , vol.108 , pp. 1-76
    • Milne, S.C.1
  • 28
    • 0001061806 scopus 로고    scopus 로고
    • A characterization of inverse relations
    • S. C. MILNE, G. BHATNAOAR (1998): A characterization of inverse relations. Discrete Math., 193:235-245.
    • (1998) Discrete Math. , vol.193 , pp. 235-245
    • Milne, S.C.1    Bhatnaoar, G.2
  • 31
    • 0001431182 scopus 로고
    • Some quadratic and cubic summation formulas for basic hypergeometric series
    • M. RAHMAN (1993): Some quadratic and cubic summation formulas for basic hypergeometric series. Canad. J. Math., 45:394-411.
    • (1993) Canad. J. Math. , vol.45 , pp. 394-411
    • Rahman, M.1
  • 32
    • 0004155375 scopus 로고
    • Reprint of the 1968 original. Huntington: R. E. Krieger.
    • J. RIORDAN (1979): Combinatorial Identities. Reprint of the 1968 original. Huntington: R. E. Krieger.
    • (1979) Combinatorial Identities
    • Riordan, J.1
  • 33
    • 0031540338 scopus 로고    scopus 로고
    • First-order analytic difference equations and integrable quantum systems
    • S.N.M. RUIJSENAARS(1997): First-order analytic difference equations and integrable quantum systems. J. Math. Phys., 38:1069-1146.
    • (1997) J. Math. Phys. , vol.38 , pp. 1069-1146
    • Ruijsenaars, S.N.M.1
  • 34
    • 21744440083 scopus 로고    scopus 로고
    • r basic hypergeometric series
    • r basic hypergeometric series. Ramanujan J., 1:243-274.
    • (1997) Ramanujan J. , vol.1 , pp. 243-274
    • Schlosser, M.1
  • 35
    • 0000369636 scopus 로고    scopus 로고
    • Summation theorems for multidimensional basic hypergeometric series by determinant evaluations
    • M. SCHLOSSER (2000): Summation theorems for multidimensional basic hypergeometric series by determinant evaluations. Discrete Math., 210:151-169.
    • (2000) Discrete Math. , vol.210 , pp. 151-169
    • Schlosser, M.1
  • 36
  • 37
    • 0004288026 scopus 로고    scopus 로고
    • Reprint of the fourth (1927) edition. Cambridge: Cambridge University Press.
    • E. T. WHITTAKER, G. N. WATSON (1996): A Course of Modem Analysis. Reprint of the fourth (1927) edition. Cambridge: Cambridge University Press.
    • (1996) A Course of Modem Analysis
    • Whittaker, E.T.1    Watson, G.N.2
  • 38
    • 0000102490 scopus 로고
    • Orthogonal functions from Cram determinants
    • J. A.WILSON (1991): Orthogonal functions from Cram determinants. SIAM J. Math. Anal., 22:1147-1155.
    • (1991) SIAM J. Math. Anal. , vol.22 , pp. 1147-1155
    • Wilson, J.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.