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Volumn 190, Issue 1, 2005, Pages 119-160

Hyperbolic beta integrals

Author keywords

Beta integrals; Hyperbolic gamma functions; Macdonald Mehta integrals

Indexed keywords


EID: 6444239366     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aim.2003.12.003     Document Type: Article
Times cited : (28)

References (26)
  • 3
    • 0002152603 scopus 로고    scopus 로고
    • On elliptic product formulas for Jackson integrals associated with reduced root systems
    • Aomoto K. On elliptic product formulas for Jackson integrals associated with reduced root systems J. Algebraic Combin. 8 2 1998 115-126
    • (1998) J. Algebraic Combin. , vol.8 , Issue.2 , pp. 115-126
    • Aomoto, K.1
  • 4
    • 84966238721 scopus 로고
    • Two integrals of Ramanujan
    • Askey R. Two integrals of Ramanujan Proc. Amer. Math. Soc. 85 2 1982 192-194
    • (1982) Proc. Amer. Math. Soc. , vol.85 , Issue.2 , pp. 192-194
    • Askey, R.1
  • 5
    • 0003041241 scopus 로고
    • Beta integrals and q-extensions
    • Ramanujan Mathematical Society, Annamalainagar (Annamalainagar, 1987), RMS Publications
    • R. Askey, Beta integrals and q-extensions, Proceedings of the Ramanujan Centennial International Conference (Annamalainagar, 1987), RMS Publications, Vol. 1, Ramanujan Mathematical Society, Annamalainagar, 1988, pp. 85-102
    • (1988) Proceedings of the Ramanujan Centennial International Conference , vol.1 , pp. 85-102
    • Askey, R.1
  • 7
    • 0001308382 scopus 로고
    • Some basic hypergeometric polynomials that generalize Jacobi polynomials
    • Askey R. Wilson J.A. Some basic hypergeometric polynomials that generalize Jacobi polynomials Mem. Amer. Math. Soc. 54 319 1985
    • (1985) Mem. Amer. Math. Soc. , vol.54 , Issue.319
    • Askey, R.1    Wilson, J.A.2
  • 8
    • 0008528631 scopus 로고    scopus 로고
    • One-dimensional double Hecke algebra and Gaussian sums
    • Cherednik I. One-dimensional double Hecke algebra and Gaussian sums Duke Math. J. 108 3 2001 511-538
    • (2001) Duke Math. J. , vol.108 , Issue.3 , pp. 511-538
    • Cherednik, I.1
  • 9
    • 2642576953 scopus 로고    scopus 로고
    • From double Hecke algebra to Fourier transform
    • Cherednik I. Ostrik V. From double Hecke algebra to Fourier transform Selecta Math. (N.S.) 9 2 2003 161-249
    • (2003) Selecta Math. (N.S.) , vol.9 , Issue.2 , pp. 161-249
    • Cherednik, I.1    Ostrik, V.2
  • 10
    • 21944450779 scopus 로고    scopus 로고
    • On certain multiple Bailey, Roger and Dougall type summation formulas
    • van Diejen J.F. On certain multiple Bailey, Roger and Dougall type summation formulas Publ. Res. Inst. Math. Sci. 33 3 1997 483-508
    • (1997) Publ. Res. Inst. Math. Sci. , vol.33 , Issue.3 , pp. 483-508
    • van Diejen, J.F.1
  • 11
    • 6444224585 scopus 로고    scopus 로고
    • Unit circle elliptic beta integrals
    • preprint, math.CA/0309279
    • J.F. van Diejen, V.P. Spiridonov, Unit circle elliptic beta integrals, preprint, 2003, math.CA/0309279
    • (2003)
    • van Diejen, J.F.1    Spiridonov, V.P.2
  • 12
    • 0001432807 scopus 로고    scopus 로고
    • Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions
    • V.I. Arnold, I.M. Gelfand, V.S. Retakh, M. Smirnov (Eds.), Boston, MA: Birkhaüser
    • Frenkel I.B. Turaev V.G. Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions. In: Arnold V.I. Gelfand I.M. Retakh V.S. Smirnov M. (Eds.). The Arnold-Gelfand Mathematical Seminars 1997 171-204 Birkhaüser Boston, MA
    • (1997) The Arnold-Gelfand Mathematical Seminars , pp. 171-204
    • Frenkel, I.B.1    Turaev, V.G.2
  • 14
    • 84968507727 scopus 로고
    • A generalization of Selberg's beta integral
    • Gustafson R.A. A generalization of Selberg's beta integral Bull. Amer. Math. Soc. (N.S.) 22 1990 97-105
    • (1990) Bull. Amer. Math. Soc. (N.S.) , vol.22 , pp. 97-105
    • Gustafson, R.A.1
  • 15
    • 84966244798 scopus 로고
    • Some q-beta and Mellin-Barnes integrals on compact Lie groups and Lie algebras
    • Gustafson R.A. Some q-beta and Mellin-Barnes integrals on compact Lie groups and Lie algebras Trans. Amer. Math. Soc. 341 1 1994 69-119
    • (1994) Trans. Amer. Math. Soc. , vol.341 , Issue.1 , pp. 69-119
    • Gustafson, R.A.1
  • 16
    • 0001360108 scopus 로고
    • Projection formulas, a reproducing kernel and a generating function for q-Wilson polynomials
    • Nassrallah B. Rahman M. Projection formulas, a reproducing kernel and a generating function for q-Wilson polynomials SIAM J. Math. Anal. 16 1985 186-197
    • (1985) SIAM J. Math. Anal. , vol.16 , pp. 186-197
    • Nassrallah, B.1    Rahman, M.2
  • 17
    • 0040822232 scopus 로고    scopus 로고
    • Integral solutions of hypergeometric q-difference systems with |q| = 1
    • (Nagoya), World Science Publishing, River Edge, NJ
    • M. Nishizawa, K. Ueno, Integral solutions of hypergeometric q-difference systems with |q| = 1, Physics and Combinatorics 1999 (Nagoya), World Science Publishing, River Edge, NJ, 2001, pp. 273-286
    • (2001) Physics and Combinatorics 1999 , pp. 273-286
    • Nishizawa, M.1    Ueno, K.2
  • 18
    • 0000946162 scopus 로고
    • 9 rational functions
    • 9 rational functions Canad. J. Math. 38 2 1986 605-618
    • (1986) Canad. J. Math. , vol.38 , Issue.2 , pp. 605-618
    • Rahman, M.1
  • 19
    • 0031540338 scopus 로고    scopus 로고
    • First order analytic difference equations and integrable quantum systems
    • Ruijsenaars S.N.M. 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
  • 20
    • 0033517395 scopus 로고    scopus 로고
    • A generalized hypergeometric function satisfying four analytic difference equations of Askey-Wilson type
    • Ruijsenaars S.N.M. A generalized hypergeometric function satisfying four analytic difference equations of Askey-Wilson type Commun. Math. Phys. 206 3 1999 639-690
    • (1999) Commun. Math. Phys. , vol.206 , Issue.3 , pp. 639-690
    • Ruijsenaars, S.N.M.1
  • 21
    • 6444228246 scopus 로고    scopus 로고
    • A generalized hypergeometric function III. Associated Hilbert space transform
    • preprint
    • S.N.M. Ruijsenaars, A generalized hypergeometric function III. Associated Hilbert space transform, preprint, 2003
    • (2003)
    • Ruijsenaars, S.N.M.1
  • 22
    • 0000404523 scopus 로고
    • On a Kronecker limit formula for real quadratic fields
    • Shintani T. On a Kronecker limit formula for real quadratic fields J. Fac. Sci. Univ. Tokyo, Sect. 1A 24 1977 167-199
    • (1977) J. Fac. Sci. Univ. Tokyo, Sect. 1A , vol.24 , pp. 167-199
    • Shintani, T.1
  • 23
    • 0035599384 scopus 로고    scopus 로고
    • On the elliptic beta function
    • Spiridonov V.P. On the elliptic beta function Russian Math. Surveys 56 2001 185-186
    • (2001) Russian Math. Surveys , vol.56 , pp. 185-186
    • Spiridonov, V.P.1
  • 24
    • 0034349855 scopus 로고    scopus 로고
    • Spectral transformation chains and some new biorthogonal rational functions
    • Spiridonov V.P. Zhedanov A. Spectral transformation chains and some new biorthogonal rational functions Commun. Math. Phys. 210 2000 49-83
    • (2000) Commun. Math. Phys. , vol.210 , pp. 49-83
    • Spiridonov, V.P.1    Zhedanov, A.2
  • 25
    • 0036190173 scopus 로고    scopus 로고
    • An expansion formula for the Askey-Wilson function
    • Stokman J.V. An expansion formula for the Askey-Wilson function J. Approx. Theory 114 2 2002 308-342
    • (2002) J. Approx. Theory , vol.114 , Issue.2 , pp. 308-342
    • Stokman, J.V.1
  • 26
    • 6444226864 scopus 로고    scopus 로고
    • Askey-Wilson functions and quantum groups
    • preprint, math.QA/0301330, in: to appear "Theory and Applications of Special Functions. A Volume Dedicated to Mizan Rahman"
    • J.V. Stokman, Askey-Wilson functions and quantum groups, preprint, 2003, math.QA/0301330, in: "Theory and Applications of Special Functions. A volume dedicated to Mizan Rahman", Developments in Mathematics, to appear
    • (2003) Developments in Mathematics
    • Stokman, J.V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.