메뉴 건너뛰기




Volumn 13, Issue 1-3, 2007, Pages 389-405

Some systems of multivariable orthogonal q-Racah polynomials

Author keywords

Dual q Hahn; Multivariable basic hypergeometric orthogonal polynomials; Multivariable discrete orthogonal polynomials; Multivariable q Racah; q Charlier polynomials; q Hahn; q Krawtchouk; q Meixner; Several variables

Indexed keywords


EID: 33845732591     PISSN: 13824090     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11139-006-0259-8     Document Type: Conference Paper
Times cited : (89)

References (26)
  • 1
    • 0001066491 scopus 로고
    • A set of orthogonal polynomials that generalize the Racah coefficients or 6- j symbols
    • Askey, R., Wilson, J.A.: A set of orthogonal polynomials that generalize the Racah coefficients or 6- j symbols. SIAM J. Math. Anal. 10, 1008-1016 (1979)
    • (1979) SIAM J. Math. Anal. , vol.10 , pp. 1008-1016
    • Askey, R.1    Wilson, J.A.2
  • 2
    • 0001308382 scopus 로고
    • Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
    • Askey, R., Wilson, J.A.: Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Memoirs Amer. Math. Soc. 319, (1985)
    • (1985) Memoirs Amer. Math. Soc. , vol.319
    • Askey, R.1    Wilson, J.A.2
  • 3
    • 0038478156 scopus 로고    scopus 로고
    • Multivariable q-Racah polynomials
    • van Diejen, J.F., Stokman, J.V.: Multivariable q-Racah polynomials. Duke Math. J. 91, 89-136 (1998)
    • (1998) Duke Math. J. , vol.91 , pp. 89-136
    • Van Diejen, J.F.1    Stokman, J.V.2
  • 4
    • 0040522335 scopus 로고
    • Orthogonal polynomials in two variables of q-Hahn and q-Jacobi type
    • Dunkl, C.F.: Orthogonal polynomials in two variables of q-Hahn and q-Jacobi type. SIAM J. Alg. Disc. Meth. 1, 137-151 (1980)
    • (1980) SIAM J. Alg. Disc. Meth. , vol.1 , pp. 137-151
    • Dunkl, C.F.1
  • 6
    • 0010531195 scopus 로고
    • Positivity and special functions
    • Askey, R. (ed.), Academic Press, New York
    • Gasper, G.: Positivity and special functions. In: Askey, R. (ed.) Theory and Applications of Special Functions, pp. 375-433. Academic Press, New York (1975)
    • (1975) Theory and Applications of Special Functions , pp. 375-433
    • Gasper, G.1
  • 7
    • 33845781336 scopus 로고
    • Nonnegative kernels in product formulas for q-Racah polynomials
    • Gasper, G., Rahman, M.: Nonnegative kernels in product formulas for q-Racah polynomials. J. Math. Anal. Appl. 95, 304-318 (1983)
    • (1983) J. Math. Anal. Appl. , vol.95 , pp. 304-318
    • Gasper, G.1    Rahman, M.2
  • 8
    • 0039860815 scopus 로고
    • Product formulas of Watson, Bailey and Bateman types and positivity of the Poisson kernel for q-Racah polynomials
    • Gasper, G., Rahman, M.: Product formulas of Watson, Bailey and Bateman types and positivity of the Poisson kernel for q-Racah polynomials. SIAM J. Math. Anal. 15, 768-789 (1984)
    • (1984) SIAM J. Math. Anal. , vol.15 , pp. 768-789
    • Gasper, G.1    Rahman, M.2
  • 10
    • 33845742792 scopus 로고    scopus 로고
    • q-Analogues of some multivariable biorthogonal polynomials
    • Ismail, M.E.H., Koelink, E. (eds.) Theory and Applications of Special Functions. A volume dedicated to Mizan Rahman
    • Gasper, G., Rahman, M.: q-Analogues of some multivariable biorthogonal polynomials. In: Ismail, M.E.H., Koelink, E. (eds.) Theory and Applications of Special Functions. A volume dedicated to Mizan Rahman. Dev. Math. vol. 13, pp. 185-208 (2005)
    • (2005) Dev. Math. , vol.13 , pp. 185-208
    • Gasper, G.1    Rahman, M.2
  • 11
    • 33845756995 scopus 로고    scopus 로고
    • Some systems of multivariable orthogonal Askey-Wilson polynomials
    • Ismail, M.E.H., Koelink, E. (eds.) Theory and Applications of Special Functions. A volume dedicated to Mizan Rahman
    • Gasper, G., Rahman, M.: Some systems of multivariable orthogonal Askey-Wilson polynomials. In: Ismail, M.E.H., Koelink, E. (eds.) Theory and Applications of Special Functions. A volume dedicated to Mizan Rahman. Dev. Math. vol. 13, pp. 209-219 (2005)
    • (2005) Dev. Math. , vol.13 , pp. 209-219
    • Gasper, G.1    Rahman, M.2
  • 13
    • 0010964267 scopus 로고
    • A Whipple's transformation for hypergeometric series in U(n) and multivariable hypergeometric orthogonal polynomials
    • Gustafson, R.A.: A Whipple's transformation for hypergeometric series in U(n) and multivariable hypergeometric orthogonal polynomials. SIAM J. Math. Anal. 18, 495-530 (1987)
    • (1987) SIAM J. Math. Anal. , vol.18 , pp. 495-530
    • Gustafson, R.A.1
  • 14
    • 0002344242 scopus 로고
    • Linear growth models with many types and multidimensional Hahn polynomials
    • Askey, R. (ed.). Academic Press, New York
    • Karlin, S., McGregor, J.: Linear growth models with many types and multidimensional Hahn polynomials. In: Askey, R. (ed.) Theory and Applications of Special Functions, pp. 261-288. Academic Press, New York (1975)
    • (1975) Theory and Applications of Special Functions , pp. 261-288
    • Karlin, S.1    McGregor, J.2
  • 16
    • 0032383984 scopus 로고    scopus 로고
    • Convolutions for orthogonal polynomials from Lie and quantum algebra representations
    • Koelink, H.T., Van der Jeugt, J.: Convolutions for orthogonal polynomials from Lie and quantum algebra representations. SIAM J. Math. Anal. 29, 794-822 (1998)
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 794-822
    • Koelink, H.T.1    Van Der Jeugt, J.2
  • 17
    • 0000515270 scopus 로고    scopus 로고
    • Askey-Wilson polynomials for root systems of type BC
    • Koornwinder, T.H.: Askey-Wilson polynomials for root systems of type BC. Contemp. Math. 138, 189-204 (1998)
    • (1998) Contemp. Math. , vol.138 , pp. 189-204
    • Koornwinder, T.H.1
  • 18
    • 33845778223 scopus 로고    scopus 로고
    • Multivariable q-Hahn polynomials as coupling coefficients for quantum algebra representations
    • Rosengren, H.: Multivariable q-Hahn polynomials as coupling coefficients for quantum algebra representations. Int. J. Math. Math. Sci. 28, 331-358 (2001)
    • (2001) Int. J. Math. Math. Sci. , vol.28 , pp. 331-358
    • Rosengren, H.1
  • 20
    • 23044518605 scopus 로고    scopus 로고
    • On BC type basic hypergeometric orthogonal polynomials
    • Stokman, J.V.: On BC type basic hypergeometric orthogonal polynomials. Trans. Amer. Math. Soc. 352, 1527-1579 (2000)
    • (2000) Trans. Amer. Math. Soc. , vol.352 , pp. 1527-1579
    • Stokman, J.V.1
  • 21
    • 0038106951 scopus 로고
    • Multivariable Wilson polynomials
    • Tratnik, M.V.: Multivariable Wilson polynomials. J. Math. Phys. 30, 2001-2011 (1989)
    • (1989) J. Math. Phys. , vol.30 , pp. 2001-2011
    • Tratnik, M.V.1
  • 22
    • 0038783942 scopus 로고
    • Multivariable biorthogonal continuous - Discrete Wilson and Racah polynomials
    • Tratnik, M.V.: Multivariable biorthogonal continuous - discrete Wilson and Racah polynomials. J. Math. Phys. 31, 1559-1575 (1990)
    • (1990) J. Math. Phys. , vol.31 , pp. 1559-1575
    • Tratnik, M.V.1
  • 23
    • 0009206913 scopus 로고
    • Some multivariable orthogonal polynomials of the Askey tableau - Continuous families
    • Tratnik, M.V.: Some multivariable orthogonal polynomials of the Askey tableau - continuous families. J. Math. Phys. 32, 2065-2073 (1991)
    • (1991) J. Math. Phys. , vol.32 , pp. 2065-2073
    • Tratnik, M.V.1
  • 24
    • 0009125166 scopus 로고
    • Some multivariable orthogonal polynomials of the Askey tableau - Discrete families
    • Tratnik, M.V.: Some multivariable orthogonal polynomials of the Askey tableau - discrete families. J. Math. Phys. 32, 2337-2342 (1991)
    • (1991) J. Math. Phys. , vol.32 , pp. 2337-2342
    • Tratnik, M.V.1
  • 25
    • 0001082444 scopus 로고
    • Some hypergeometric orthogonal polynomials
    • Wilson, J.A.: Some hypergeometric orthogonal polynomials. SIAM J. Math. Anal. 11, 690-701 (1980)
    • (1980) SIAM J. Math. Anal. , vol.11 , pp. 690-701
    • Wilson, J.A.1
  • 26
    • 4344712043 scopus 로고    scopus 로고
    • On discrete orthogonal polynomials of several variables
    • Xu, Y.: On discrete orthogonal polynomials of several variables. Adv. in Appl. Math. 33, 615-632 (2004)
    • (2004) Adv. in Appl. Math. , vol.33 , pp. 615-632
    • Xu, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.