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Volumn 210, Issue 1-3, 2000, Pages 151-169

Summation theorems for multidimensional basic hypergeometric series by determinant evaluations

Author keywords

Ar series; Basic hypergeometric; Cr series; Determinants; Multidimensional summation theorems, associated to root systems

Indexed keywords


EID: 0000369636     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(99)00125-9     Document Type: Article
Times cited : (30)

References (29)
  • 1
    • 0016115402 scopus 로고
    • Applications of basic hypergeometric functions
    • G.E. Andrews, Applications of basic hypergeometric functions, SIAM Rev. 16 (1974) 441-484.
    • (1974) SIAM Rev. , vol.16 , pp. 441-484
    • Andrews, G.E.1
  • 2
    • 0000271809 scopus 로고
    • Series of hypergeometric type which are infinite in both directions
    • Oxford
    • W.N. Bailey, Series of hypergeometric type which are infinite in both directions, Quart. J. Math. (Oxford) 7 (1936) 105-115.
    • (1936) Quart. J. Math. , vol.7 , pp. 105-115
    • Bailey, W.N.1
  • 5
    • 21344485564 scopus 로고
    • Partial fractions and bilateral summations
    • W.C. Chu, Partial fractions and bilateral summations, J. Math. Phys. 35 (1994) 2036-2042.
    • (1994) J. Math. Phys. , vol.35 , pp. 2036-2042
    • Chu, W.C.1
  • 7
    • 0000267209 scopus 로고
    • Summation formulas for basic hypergeometric series
    • G. Gasper, Summation formulas for basic hypergeometric series, SIAM J. Math. Anal. 12 (1981) 196-200.
    • (1981) SIAM J. Math. Anal. , vol.12 , pp. 196-200
    • Gasper, G.1
  • 10
    • 0001726277 scopus 로고
    • The Macdonald identities for affine root systems of classical type and hypergeometric series very well-poised on semi-simple Lie algebras
    • N.K. Thakare (Ed.), Dec. 26th to 28th, 1987, Pune, India
    • R.A. Gustafson, The Macdonald identities for affine root systems of classical type and hypergeometric series very well-poised on semi-simple Lie algebras, in: N.K. Thakare (Ed.), Ramanujan International Symposium on Analysis, Dec. 26th to 28th, 1987, Pune, India, 1989, pp. 187-224.
    • (1989) Ramanujan International Symposium on Analysis , pp. 187-224
    • Gustafson, R.A.1
  • 11
    • 0030121809 scopus 로고    scopus 로고
    • Heine transformations for a new kind of basic hypergeometric series in U(n)
    • R.A. Gustafson, C. Krattenthaler, Heine transformations for a new kind of basic hypergeometric series in U(n), J. Comput. Appl. Math. 68 (1996) 151-158.
    • (1996) J. Comput. Appl. Math. , vol.68 , pp. 151-158
    • Gustafson, R.A.1    Krattenthaler, C.2
  • 12
    • 0013016828 scopus 로고    scopus 로고
    • 1-transformations
    • M.E.H. Ismail, D.R. Masson, M. Rahman (Eds.) Amer. Math. Soc., Providence, RI, Fields Institute Communications
    • 1-transformations, in: M.E.H. Ismail, D.R. Masson, M. Rahman (Eds.) Special Functions, q-Series and Related Topics, Amer. Math. Soc., Providence, RI, Fields Institute Communications, vol. 14, 1997, pp. 83-90.
    • (1997) Special Functions, q-Series and Related Topics , vol.14 , pp. 83-90
    • Gustafson, R.A.1    Krattenthaler, C.2
  • 13
    • 0030524994 scopus 로고    scopus 로고
    • Rook theory and hypergeometric series
    • J. Haglund, Rook theory and hypergeometric series, Adv. Appl. Math. 17 (1996) 408-459.
    • (1996) Adv. Appl. Math. , vol.17 , pp. 408-459
    • Haglund, J.1
  • 14
    • 0004250391 scopus 로고
    • Cambridge University Press, Cambridge, reprinted by Chelsea, New York
    • G.H. Hardy, Ramanujan, Cambridge University Press, Cambridge, 1940, reprinted by Chelsea, New York, 1978.
    • (1940) Ramanujan
    • Hardy, G.H.1
  • 15
    • 84966247454 scopus 로고
    • A simple proof of Ramanujan's 1ψ1 sum
    • M.E.H. Ismail, A simple proof of Ramanujan's 1ψ1 sum, Proc. Amer. Math. Soc. 63 (1977) 185-186.
    • (1977) Proc. Amer. Math. Soc. , vol.63 , pp. 185-186
    • Ismail, M.E.H.1
  • 16
    • 0000437438 scopus 로고
    • Transformations of q-series
    • F.H. Jackson, Transformations of q-series, Messenger Math. 39 (1910) 145-153.
    • (1910) Messenger Math. , vol.39 , pp. 145-153
    • Jackson, F.H.1
  • 17
    • 0001311498 scopus 로고
    • Summation of q-hypergeometric series
    • F.H. Jackson, Summation of q-hypergeometric series, Messenger Math. 57 (1921) 101-112.
    • (1921) Messenger Math. , vol.57 , pp. 101-112
    • Jackson, F.H.1
  • 18
    • 0000474360 scopus 로고
    • Hypergeometric functions with integral parameter differences
    • Per W. Karlsson, Hypergeometric functions with integral parameter differences, J. Math. Phys. 12 (1971) 270-271.
    • (1971) J. Math. Phys. , vol.12 , pp. 270-271
    • Karlsson, P.W.1
  • 19
    • 0003321117 scopus 로고
    • 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 , Issue.552
    • Krattenthaler, C.1
  • 20
    • 0002912280 scopus 로고
    • 1 sum
    • G.E. Andrews et al. (Eds.), Academic Press, New York
    • 1 sum, in: G.E. Andrews et al. (Eds.), Ramanujan Revisited, Academic Press, New York, 1988, pp. 473-524.
    • (1988) Ramanujan Revisited , pp. 473-524
    • Milne, S.C.1
  • 21
    • 0031572791 scopus 로고    scopus 로고
    • 2 summation theorems for U(n) basic hypergeometric series
    • 2 summation theorems for U(n) basic hypergeometric series, Adv. Math. 131 (1997) 93-187.
    • (1997) Adv. Math. , vol.131 , pp. 93-187
    • Milne, S.C.1
  • 22
    • 0001132088 scopus 로고
    • l Bailey transform and Bailey lemma
    • l Bailey transform and Bailey lemma, Discrete Math. 139 (1995) 319-346.
    • (1995) Discrete Math. , vol.139 , pp. 319-346
    • Milne, S.C.1    Lilly, G.M.2
  • 23
    • 0000016826 scopus 로고
    • Generalized hypergeometric function of unit argument
    • B.M. Minton, Generalized hypergeometric function of unit argument, J. Math. Phys. 11 (1970) 1375-1376.
    • (1970) J. Math. Phys. , vol.11 , pp. 1375-1376
    • Minton, B.M.1
  • 24
    • 0345747958 scopus 로고
    • Obversationes analyticae ad L.
    • Historia de
    • J.F. Pfaff, Obversationes analyticae ad L. Euler Institutiones Calculi Integralis, vol. IV, Supplem. II et IV, Historia de 1793; Nova acta acad. sci. Petropolitanae, vol. 11, 1797, pp. 38-57.
    • (1793) Euler Institutiones Calculi Integralis , vol.4 , Issue.2-4 SUPPL.
    • Pfaff, J.F.1
  • 25
    • 0042784809 scopus 로고
    • J.F. Pfaff, Obversationes analyticae ad L. Euler Institutiones Calculi Integralis, vol. IV, Supplem. II et IV, Historia de 1793; Nova acta acad. sci. Petropolitanae, vol. 11, 1797, pp. 38-57.
    • (1797) Nova Acta Acad. Sci. Petropolitanae , vol.11 , pp. 38-57
  • 28
    • 0005631246 scopus 로고
    • General transformations of bilateral series
    • Oxford
    • L.J. Slater, General transformations of bilateral series, Quart. J. Math. (Oxford) 3 (1952) 73-80.
    • (1952) Quart. J. Math. , vol.3 , pp. 73-80
    • Slater, L.J.1
  • 29
    • 0000102490 scopus 로고
    • Orthogonal functions from Gram determinants
    • J.A. Wilson, Orthogonal functions from Gram determinants, SIAM J. Math. Anal. 22 (1991) 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.