메뉴 건너뛰기




Volumn 275, Issue 1, 2007, Pages 37-95

Properties of generalized univariate hypergeometric functions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 34547843623     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-007-0289-0     Document Type: Article
Times cited : (40)

References (38)
  • 2
    • 21344479784 scopus 로고
    • Integrability of difference Calogero-Moser systems
    • 6
    • Diejen J.F. (1994). Integrability of difference Calogero-Moser systems. J. Math. Phys. 35(6): 2983-3004
    • (1994) J. Math. Phys. , vol.35 , pp. 2983-3004
    • Van Diejen, J.F.1
  • 3
    • 0038345715 scopus 로고    scopus 로고
    • Modular double of a Quantum Group
    • "Conférence Moshé Flato" 1999, Vol I (Dijon) Dordrecht: Kluwer Acad. Publ.
    • Faddeev, L.: Modular double of a Quantum Group. In: "Confé rence Moshé Flato" 1999, Vol I (Dijon), Math. Phys. Stud. 21, Dordrecht: Kluwer Acad. Publ., 2000, pp. 149-156
    • (2000) Math. Phys. Stud. , vol.21 , pp. 149-156
    • Faddeev, L.1
  • 4
    • 0001432807 scopus 로고    scopus 로고
    • Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions
    • Arnold, V.I., Gelfand, I.M., Retakh, V.S., Smirnov, M. (eds.) Birkhäuser, Boston
    • Frenkel, I.N., 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., pp. 171-204. Birkhäuser, Boston, 1997
    • (1997) The Arnold-Gelfand Mathematical Seminars , pp. 171-204
    • Frenkel, I.N.1    Turaev, V.G.2
  • 6
    • 0344253658 scopus 로고    scopus 로고
    • The Wilson function transform
    • 52
    • Groenevelt W. (2003). The Wilson function transform. Int. Math. Res. Not. 2003(52): 2779-2817
    • (2003) Int. Math. Res. Not. , vol.2003 , pp. 2779-2817
    • Groenevelt, W.1
  • 7
    • 21944434494 scopus 로고    scopus 로고
    • Contiguous relations, continued fractions and orthogonality
    • 2
    • Gupta D.P. and Masson D.R. (1998). Contiguous relations, continued fractions and orthogonality. Trans. Amer. Math. Soc. 350(2): 769-808
    • (1998) Trans. Amer. Math. Soc. , vol.350 , pp. 769-808
    • Gupta, D.P.1    Masson, D.R.2
  • 8
  • 10
    • 84986222910 scopus 로고    scopus 로고
    • Fourier transforms on the quantum SU(1,1) quantum group (with an appendix of M. Rahman)
    • 4
    • Koelink E. and Stokman J.V. (2001). Fourier transforms on the quantum SU(1,1) quantum group (with an appendix of M. Rahman). Publ. Res. Math. Sci. 37(4): 621-715
    • (2001) Publ. Res. Math. Sci. , vol.37 , pp. 621-715
    • Koelink, E.1    Stokman, J.V.2
  • 11
    • 0008592263 scopus 로고    scopus 로고
    • The Askey-Wilson function transform
    • 22
    • Koelink E. and Stokman J.V. (2001). The Askey-Wilson function transform. Int. Math. Res. Not. 2001(22): 1203-1227
    • (2001) Int. Math. Res. Not. , vol.2001 , pp. 1203-1227
    • Koelink, E.1    Stokman, J.V.2
  • 12
    • 1842538819 scopus 로고    scopus 로고
    • Elliptic U(2) quantum group and elliptic hypergeometric series
    • 3
    • Koelink E., Rosengren H. and Norden Y. (2004). Elliptic U(2) quantum group and elliptic hypergeometric series. Commun Math. Phys 245(3): 519-537
    • (2004) Commun Math. Phys , vol.245 , pp. 519-537
    • Koelink, E.1    Van Norden, Y.2    Rosengren, H.3
  • 13
    • 0031582460 scopus 로고    scopus 로고
    • Quantum integrability of the generalized elliptic Ruijsenaars models
    • Komori Y. and Hikami K. (1997). Quantum integrability of the generalized elliptic Ruijsenaars models. J. Phys. A: Math. Gen. 30: 4341-4364
    • (1997) J. Phys. A: Math. Gen. , vol.30 , pp. 4341-4364
    • Komori, Y.1    Hikami, K.2
  • 14
    • 15844376697 scopus 로고    scopus 로고
    • Quantum zonal spherical functions and Macdonald polynomials
    • 1
    • Letzter G. (2004). Quantum zonal spherical functions and Macdonald polynomials. Adv. Math. 189(1): 88-147
    • (2004) Adv. Math. , vol.189 , pp. 88-147
    • Letzter, G.1
  • 16
    • 0742316538 scopus 로고    scopus 로고
    • Orthogonal polynomials associated to root systems
    • Art. B45a
    • Macdonald, I.G.: Orthogonal polynomials associated to root systems. Sém. Lothar. Combin. 45, Art. B45a (2000/01)
    • (2000) Sém. Lothar. Combin. , vol.45
    • MacDonald, I.G.1
  • 17
    • 0001360108 scopus 로고
    • Projection formulas, a reproducing kernel and a generating function for q-Wilson polynomials
    • Nassrallah B. and Rahman M. (1985). Projection formulas, a reproducing kernel and a generating function for q-Wilson polynomials. SIAM J. Math. Anal. 16: 186-197
    • (1985) SIAM J. Math. Anal. , vol.16 , pp. 186-197
    • Nassrallah, B.1    Rahman, M.2
  • 18
    • 0030588041 scopus 로고    scopus 로고
    • Macdonald's symmetric polynomials and as zonal spherical functions on some quantum homogeneous spaces
    • 1
    • Noumi M. (1996). Macdonald's symmetric polynomials and as zonal spherical functions on some quantum homogeneous spaces. Adv. Math. 123(1): 16-77
    • (1996) Adv. Math. , vol.123 , pp. 16-77
    • Noumi, M.1
  • 20
    • 0000946162 scopus 로고
    • 9 rational functions
    • 9 rational functions. Canad. J. Math. 38: 605-618
    • (1986) Canad. J. Math. , vol.38 , pp. 605-618
    • Rahman, M.1
  • 21
    • 63449087992 scopus 로고    scopus 로고
    • Tranformations of elliptic hypergeometric integrals
    • to appear
    • Rains, E.M.: Tranformations of elliptic hypergeometric integrals. Ann. Math., to appear 2008
    • (2008) Ann. Math.
    • Rains, E.M.1
  • 22
    • 33750616917 scopus 로고    scopus 로고
    • Recurrences for elliptic hypergeometric integrals in elliptic integrable systems
    • Noumi, M., Takasaki, K. (eds.) Kobe, Japan
    • Rains, E.M.: Recurrences for elliptic hypergeometric integrals in elliptic integrable systems. In: Noumi, M., Takasaki, K. (eds.) Rokko Lectures in Mathematics 18, pp. 183-199, Kobe, Japan (2005)
    • (2005) Rokko Lectures in Mathematics , vol.18 , pp. 183-199
    • Rains, E.M.1
  • 24
    • 0031540338 scopus 로고    scopus 로고
    • First order analytic difference equations and integrable quantum systems
    • Ruijsenaars S.N.M. (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
  • 25
    • 0001941773 scopus 로고    scopus 로고
    • Systems of Calogero-Moser type
    • Particles and Fields (Banff, AB, 1994) New York: Springer
    • Ruijsenaars, S.N.M.: Systems of Calogero-Moser type. In: Particles and Fields (Banff, AB, 1994), CRM Ser. Math. Phys., New York: Springer, 1999, pp. 251-352
    • (1999) CRM Ser. Math. Phys. , pp. 251-352
    • Ruijsenaars, S.N.M.1
  • 26
    • 0033517395 scopus 로고    scopus 로고
    • A generalized hypergeometric function satisfying four analytic difference equations of Askey-Wilson type
    • 3
    • Ruijsenaars S.N.M. (1999). A generalized hypergeometric function satisfying four analytic difference equations of Askey-Wilson type. Commun Math. Phys. 206(3): 639-690
    • (1999) Commun Math. Phys. , vol.206 , pp. 639-690
    • Ruijsenaars, S.N.M.1
  • 27
    • 0347173801 scopus 로고    scopus 로고
    • Special functions defined by analytic difference equations
    • Special functions 2000: Current perspective and future directions (Tempe, AZ) Dordrecht: Kluwer Acad. Publ.
    • Ruijsenaars, S.N.M.: Special functions defined by analytic difference equations. In: Special functions 2000: Current perspective and future directions (Tempe, AZ), NATO Sci. Ser. II Math. Phys. Chem. 30, Dordrecht: Kluwer Acad. Publ., 2001, pp. 281-333
    • (2001) NATO Sci. Ser. II Math. Phys. Chem. , vol.30 , pp. 281-333
    • Ruijsenaars, S.N.M.1
  • 29
    • 0346308634 scopus 로고    scopus 로고
    • A generalized hypergeometric function III. Associated Hilbert space transform
    • 3
    • Ruijsenaars S.N.M. (2003). A generalized hypergeometric function III. Associated Hilbert space transform. Commun. Math. Phys. 243(3): 413-448
    • (2003) Commun. Math. Phys. , vol.243 , pp. 413-448
    • Ruijsenaars, S.N.M.1
  • 30
    • 0000404523 scopus 로고
    • On a Kronecker limit formula for real quadratic fields
    • Shintani T. (1977). On a Kronecker limit formula for real quadratic fields. J. Fac. Sci. Univ. Tokyo, Sect. 1A 24: 167-199
    • (1977) J. Fac. Sci. Univ. Tokyo, Sect. 1A , vol.24 , pp. 167-199
    • Shintani, T.1
  • 31
    • 0035599384 scopus 로고    scopus 로고
    • On the elliptic beta function
    • 1
    • Spiridonov V.P. (2001). On the elliptic beta function. Russ. Math. Surv. 56(1): 185-186
    • (2001) Russ. Math. Surv. , vol.56 , pp. 185-186
    • Spiridonov, V.P.1
  • 32
    • 33845759276 scopus 로고    scopus 로고
    • Short proofs of the elliptic beta integrals
    • Spiridonov, V.P.: Short proofs of the elliptic beta integrals. Ramanujan J. 13, 265-283 (2007)
    • (2007) Ramanujan J. , vol.13 , pp. 265-283
    • Spiridonov, V.P.1
  • 33
    • 34547845765 scopus 로고    scopus 로고
    • Classical elliptic hypergeometric functions and their applications
    • Dept. of Mth., Kobe Univ.
    • Spiridonov, V.P.: Classical elliptic hypergeometric functions and their applications. Rokko Lect. in Math. Vol. 18, Dept. of Mth., Kobe Univ., 2005, pp. 253-287
    • (2005) Rokko Lect. in Math. , vol.18 , pp. 253-287
    • Spiridonov, V.P.1
  • 34
    • 3843146673 scopus 로고    scopus 로고
    • Theta hypergeometric integrals
    • Spiridonov, V.P.: Theta hypergeometric integrals. Algebra i Analiz 15, 161-215 (2003)
    • (2003) Algebra i Analiz , vol.15 , pp. 161-215
    • Spiridonov, V.P.1
  • 36
    • 0034349855 scopus 로고    scopus 로고
    • Spectral transformation chains and some new biorthogonal rational functions
    • Spiridonov V.P. and Zhedanov A.S. (2000). Spectral transformation chains and some new biorthogonal rational functions. Commun Math. Phys. 210: 49-83
    • (2000) Commun Math. Phys. , vol.210 , pp. 49-83
    • Spiridonov, V.P.1    Zhedanov, A.S.2
  • 37
    • 2642548459 scopus 로고    scopus 로고
    • Difference Fourier transforms for nonreduced root systems
    • 3
    • Stokman J.V. (2003). Difference Fourier transforms for nonreduced root systems. Selecta Math. (N.S.) 9(3): 409-494
    • (2003) Selecta Math. (N.S.) , vol.9 , pp. 409-494
    • Stokman, J.V.1
  • 38
    • 6444239366 scopus 로고    scopus 로고
    • Hyperbolic beta integrals
    • Stokman J.V. (2005). Hyperbolic beta integrals. Adv. Math. 190: 119-160
    • (2005) Adv. Math. , vol.190 , pp. 119-160
    • Stokman, J.V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.