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Volumn 107, Issue 2, 1999, Pages 219-232

The factorization method for the Askey-Wilson polynomials

Author keywords

Askey Wilson polynomial; Infeld Hull factorization method

Indexed keywords

DIFFERENCE EQUATIONS; MATHEMATICAL OPERATORS; POLYNOMIALS; PROBLEM SOLVING;

EID: 0032639597     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(99)00090-4     Document Type: Article
Times cited : (21)

References (27)
  • 1
    • 0001308382 scopus 로고
    • Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
    • Askey R., Wilson J. Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Mem. Amer. Math. Soc. 54:1985;1-55.
    • (1985) Mem. Amer. Math. Soc. , vol.54 , pp. 1-55
    • Askey, R.1    Wilson, J.2
  • 2
    • 0002321229 scopus 로고
    • Difference hypergeometric functions
    • in: A.A. Gonchar, E.B. Saff (Eds.) Springer, Berlin
    • N.M. Atakishiyev, S.K. Suslov, Difference hypergeometric functions, in: A.A. Gonchar, E.B. Saff (Eds.), Progress in Approximation Theory, Springer, Berlin, 1992, pp. 1-35.
    • (1992) Progress in Approximation Theory , pp. 1-35
    • Atakishiyev, N.M.1    Suslov, S.K.2
  • 3
    • 0032489191 scopus 로고    scopus 로고
    • Discrete Darboux transformation for discrete polynomials of hypergeometric type
    • Bangerezako G. Discrete Darboux transformation for discrete polynomials of hypergeometric type. J. Phys. A. 31:1998;1-6.
    • (1998) J. Phys. a , vol.31 , pp. 1-6
    • Bangerezako, G.1
  • 6
    • 0039024372 scopus 로고    scopus 로고
    • PhD thesis, Dept. Math., UCL, to be presented in July
    • G. Bangerezako, PhD thesis, Dept. Math., UCL, to be presented in July 1999.
    • (1999)
    • Bangerezako, G.1
  • 7
    • 21844510342 scopus 로고    scopus 로고
    • The Askey-Wilson polynomials and q -Sturm-Liouville problems
    • Brown B., Evans W., Ismail M. The Askey-Wilson polynomials and. q -Sturm-Liouville problems Math. Proc. Camb. Phil. Soc. 119(1):1996;1-16.
    • (1996) Math. Proc. Camb. Phil. Soc. , vol.119 , Issue.1 , pp. 1-16
    • Brown, B.1    Evans, W.2    Ismail, M.3
  • 9
    • 11244299230 scopus 로고
    • The factorization method
    • Infeld L., Hull T. The factorization method. Rev. Mod. Phys. 23:1951;21-68.
    • (1951) Rev. Mod. Phys. , vol.23 , pp. 21-68
    • Infeld, L.1    Hull, T.2
  • 10
    • 0347678527 scopus 로고
    • Unified theory of recurrence formulas I
    • April-June
    • T. Inui, Unified theory of recurrence formulas I, Prog. Theor. Phys. 3 (2) (1948) April-June.
    • (1948) Prog. Theor. Phys. , vol.3 , Issue.2
    • Inui, T.1
  • 11
    • 27144448175 scopus 로고
    • Symmetry techniques for q -series: Askey-Wilson polynomials
    • Kalnins E.G., Miller W. Symmetry techniques for. q -series: Askey-Wilson polynomials Rocky Mountain J. Math. 19:1989;223-230.
    • (1989) Rocky Mountain J. Math. , vol.19 , pp. 223-230
    • Kalnins, E.G.1    Miller, W.2
  • 13
    • 0040209871 scopus 로고
    • On pairs of related orthogonal polynomials sets
    • Krall H., Sheffer I. On pairs of related orthogonal polynomials sets. Math. Zeitschr. 86:1965;425-450.
    • (1965) Math. Zeitschr. , vol.86 , pp. 425-450
    • Krall, H.1    Sheffer, I.2
  • 14
    • 0001282924 scopus 로고
    • Orthogonal polynomials, duality and association schemes
    • Leonard D.A. Orthogonal polynomials, duality and association schemes. SIAM J. Math. Anal. 13(4):1982;656-663.
    • (1982) SIAM J. Math. Anal. , vol.13 , Issue.4 , pp. 656-663
    • Leonard, D.A.1
  • 15
    • 0004548025 scopus 로고
    • Associated Askey-Wilson polynomials as Laguerre-Hahn orthogonal polynomials
    • Springer, Berlin
    • A.P. Magnus, Associated Askey-Wilson polynomials as Laguerre-Hahn orthogonal polynomials, Springer Lecture Notes in Math., vol. 1329, Springer, Berlin, 1988, pp. 261-278.
    • (1988) Springer Lecture Notes in Math. , vol.1329 , pp. 261-278
    • Magnus, A.P.1
  • 16
    • 0000479720 scopus 로고    scopus 로고
    • Special non uniform lattice (snul) orthogonal polynomials on discrete dense sets of points
    • Magnus A.P. Special non uniform lattice (snul) orthogonal polynomials on discrete dense sets of points. J. Comp. Appl. Math. 65:1997;253-265.
    • (1997) J. Comp. Appl. Math. , vol.65 , pp. 253-265
    • Magnus, A.P.1
  • 17
    • 0001283637 scopus 로고
    • Differential-difference evolution equations II, Darboux transformation for the toda lattice
    • Matveev V., Salle M. Differential-difference evolution equations II, Darboux transformation for the toda lattice. Lett. Math. Phys. 3:1979;425-429.
    • (1979) Lett. Math. Phys. , vol.3 , pp. 425-429
    • Matveev, V.1    Salle, M.2
  • 18
    • 18644384272 scopus 로고
    • Lie theory and difference equations I
    • Miller W. Lie theory and difference equations I. J. Math. Anal. Appl. 28:1969;383-399.
    • (1969) J. Math. Anal. Appl. , vol.28 , pp. 383-399
    • Miller, W.1
  • 19
    • 0039024362 scopus 로고
    • Symmetry techniques and orthogonality for q -series
    • Miller W. Symmetry techniques and orthogonality for. q -series IMA volumes in Math. Appl. 18:1989;191-212.
    • (1989) IMA Volumes in Math. Appl. , vol.18 , pp. 191-212
    • Miller, W.1
  • 21
    • 0039616601 scopus 로고
    • Darboux transformation and non-classical orthogonal polynomials
    • (in Russian)
    • B. Samsonov, I. Ovcharov, Darboux transformation and non-classical orthogonal polynomials, Izv. vuzov (Fizika) 4 (1995) 58-65 (in Russian).
    • (1995) Izv. Vuzov (Fizika) , vol.4 , pp. 58-65
    • Samsonov, B.1    Ovcharov, I.2
  • 22
    • 85033952959 scopus 로고
    • Dressing chain and spectral theory of Schrödinger operator
    • Shabat A.B., Veselov A.P. Dressing chain and spectral theory of Schrödinger operator. Funct. Anal. Appl. 27:1993;81-96.
    • (1993) Funct. Anal. Appl. , vol.27 , pp. 81-96
    • Shabat, A.B.1    Veselov, A.P.2
  • 23
    • 0039024364 scopus 로고    scopus 로고
    • On factorization and algebraization of difference equations of hypergeometric type
    • in: M. Alfaro et al. (Eds.) (in honour of Professor André Ronveaux), Leganés June 24-26
    • Yu.F. Smirnov, On factorization and algebraization of difference equations of hypergeometric type, in: M. Alfaro et al. (Eds.), Proc. Internat. Workshop on Orthogonal Polynomials in Mathematical Physics (in honour of Professor André Ronveaux), Leganés June 24-26, 1996.
    • (1996) Proc. Internat. Workshop on Orthogonal Polynomials in Mathematical Physics
    • Smirnov, Yu.f.1
  • 24
    • 0039066462 scopus 로고    scopus 로고
    • Symmetries of factorization chains for the discrete Schrödinger equation
    • Spiridonov V. Symmetries of factorization chains for the discrete Schrödinger equation. J. Phys. A. 30:1997;L15-L21.
    • (1997) J. Phys. a , vol.30
    • Spiridonov, V.1
  • 25
    • 0002613167 scopus 로고
    • Difference Schrödinger operators with linear and exponential discrete spectra
    • Spiridonov V., Vinet L., Zhedanov A. Difference Schrödinger operators with linear and exponential discrete spectra. Lett. Math. Phys. 29:1993;63-73.
    • (1993) Lett. Math. Phys. , vol.29 , pp. 63-73
    • Spiridonov, V.1    Vinet, L.2    Zhedanov, A.3
  • 26
    • 21844496520 scopus 로고
    • Periodic reductions of the factorization chain and the Hahn polynomials
    • Spiridonov V., Vinet L., Zhedanov A. Periodic reductions of the factorization chain and the Hahn polynomials. J. Phys. A. 27:1994;L669-L675.
    • (1994) J. Phys. a , vol.27
    • Spiridonov, V.1    Vinet, L.2    Zhedanov, A.3
  • 27
    • 0001243950 scopus 로고
    • Discrete Darboux transformations, the discrete-time Toda lattice and the Askey-Wilson polynomials
    • Spiridonov V., Vinet L., Zhedanov A. Discrete Darboux transformations, the discrete-time Toda lattice and the Askey-Wilson polynomials. Methods Appl. Anal. 2:1995;369-398.
    • (1995) Methods Appl. Anal. , vol.2 , pp. 369-398
    • Spiridonov, V.1    Vinet, L.2    Zhedanov, A.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.