메뉴 건너뛰기




Volumn 210, Issue 1, 2000, Pages 49-83

Spectral transformation chains and some new biorthogonal rational functions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0034349855     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050772     Document Type: Article
Times cited : (84)

References (25)
  • 1
    • 0001308382 scopus 로고
    • Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
    • 1. Askey, R. and Wilson, J.A.: Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Mem. Am. Math. Soc. 54, 1-55 (1985)
    • (1985) Mem. Am. Math. Soc. , vol.54 , pp. 1-55
    • Askey, R.1    Wilson, J.A.2
  • 3
    • 0003192389 scopus 로고
    • Exactly solvable SOS models II: Proof of the star-triangle relation and combinatorial identities
    • Conformal Field Theory and Lattice Models
    • 3. Date, E., Jimbo, M., Kuniba, A., Miwa, T. and Okado, M.: Exactly solvable SOS models II: Proof of the star-triangle relation and combinatorial identities. In: Conformal Field Theory and Lattice Models, Advanced Studies in Pure Math. 16, 17-122 (1988)
    • (1988) Advanced Studies in Pure Math. , vol.16 , pp. 17-122
    • Date, E.1    Jimbo, M.2    Kuniba, A.3    Miwa, T.4    Okado, M.5
  • 4
    • 0001432807 scopus 로고    scopus 로고
    • Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions
    • Boston, MA: Birkhäuser
    • 4. Frenkel, I.B. and Turaev, V.G.: Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions. In: The Arnold-Gelfand Mathematical Seminars, Boston, MA: Birkhäuser, 1997, pp. 171-204
    • (1997) The Arnold-Gelfand Mathematical Seminars , pp. 171-204
    • Frenkel, I.B.1    Turaev, V.G.2
  • 6
    • 0002577436 scopus 로고
    • On the polynomials orthogonal with respect to a given number sequence
    • in Russian
    • 6. Geronimus, Ya.L.: On the polynomials orthogonal with respect to a given number sequence. Zap. Mat. Otdel. Khar'kov Univ. i NII Mat. i Mehan. 17, 3-18 (1940) (in Russian)
    • (1940) Zap. Mat. Otdel. Khar'kov Univ. i NII Mat. i Mehan. , vol.17 , pp. 3-18
    • Geronimus, Ya.L.1
  • 7
    • 0001185631 scopus 로고
    • On the polynomials orthogonal with respect to a given number sequence and a theorem by W. Hahn
    • 7. Geronimus, Ya.L.: On the polynomials orthogonal with respect to a given number sequence and a theorem by W. Hahn. Izv. Akad. Nauk 4, 215-228 (1940)
    • (1940) Izv. Akad. Nauk , vol.4 , pp. 215-228
    • Geronimus, Ya.L.1
  • 8
    • 21344496500 scopus 로고
    • Watson's basic analogue of Ramanujan's entry 40 and its generalization
    • 8. Gupta, D.P. and Masson, D.R.: Watson's basic analogue of Ramanujan's entry 40 and its generalization. SIAM J. Math. Anal. 25, 429-440 (1994)
    • (1994) SIAM J. Math. Anal. , vol.25 , pp. 429-440
    • Gupta, D.P.1    Masson, D.R.2
  • 9
    • 21944434494 scopus 로고    scopus 로고
    • Contiguous relations, continued fractions and orthogonality
    • 9. Gupta, D.P. and Masson, D.R.: Contiguous relations, continued fractions and orthogonality. Trans. Am. Math. Soc. 350, 769-808 (1998)
    • (1998) Trans. Am. Math. Soc. , vol.350 , pp. 769-808
    • Gupta, D.P.1    Masson, D.R.2
  • 10
    • 84966201717 scopus 로고
    • On the theory of biorthogonal polynomials
    • 10. Iserles, A. and Nørsett, S.P.: On the theory of biorthogonal polynomials. Trans. Am. Math. Soc. 306, 455-474 (1988)
    • (1988) Trans. Am. Math. Soc. , vol.306 , pp. 455-474
    • Iserles, A.1    Nørsett, S.P.2
  • 11
    • 0141820548 scopus 로고
    • Generalized orthogonality and continued fractions
    • 11. Ismail, M.E.H. and Masson, D.R.: Generalized orthogonality and continued fractions. J. Approx. Theory 83, 1-40 (1995)
    • (1995) J. Approx. Theory , vol.83 , pp. 1-40
    • Ismail, M.E.H.1    Masson, D.R.2
  • 12
    • 0000479720 scopus 로고
    • Special non uniform lattice (SNUL) orthogonal polynomials on discrete dense sets of points
    • 12. Magnus, A.: Special non uniform lattice (SNUL) orthogonal polynomials on discrete dense sets of points. J. Comp. Appl. Math. 65, 253-265 (1995)
    • (1995) J. Comp. Appl. Math. , vol.65 , pp. 253-265
    • Magnus, A.1
  • 13
    • 0000946162 scopus 로고
    • 10φ9 rational functions
    • 10φ9 rational functions. Canad. J. Math. 38, 605-618 (1986)
    • (1986) Canad. J. Math. , vol.38 , pp. 605-618
    • Rahman, M.1
  • 14
    • 0001262738 scopus 로고
    • Biorthogonality of a system of rational functions with respect to a positive measure on [-1, 1]
    • 14. Rahman, M.: Biorthogonality of a system of rational functions with respect to a positive measure on [-1, 1]. SIAM J. Math. Anal. 22, 1430-1441 (1991)
    • (1991) SIAM J. Math. Anal. , vol.22 , pp. 1430-1441
    • Rahman, M.1
  • 15
    • 0000815807 scopus 로고
    • Classical biorthogonal rational functions
    • Methods of Approximation Theory in Complex Analysis and Mathematical Physics IV, Berlin: Springer-Verlag
    • 15. Rahman, M. and Suslov, S.K.: Classical biorthogonal rational functions. In: Methods of Approximation Theory in Complex Analysis and Mathematical Physics IV, Lecture Notes in Math. 1550, Berlin: Springer-Verlag, 1993, pp. 131-146
    • (1993) Lecture Notes in Math. , vol.1550 , pp. 131-146
    • Rahman, M.1    Suslov, S.K.2
  • 16
    • 0039066462 scopus 로고    scopus 로고
    • Symmetries of factorization chains for the discrete Schrödinger equation
    • 16. Spiridonov, V.: Symmetries of factorization chains for the discrete Schrödinger equation: J. Phys. A: Math. & Gen. 30, L15-L21, (1997)
    • (1997) J. Phys. A: Math. & Gen. , vol.30
    • Spiridonov, V.1
  • 17
    • 0001243950 scopus 로고
    • Discrete Darboux transformations, discrete time Toda lattice and the Askey-Wilson polynomials
    • 17. Spiridonov, V. and Zhedanov, A.: Discrete Darboux transformations, discrete time Toda lattice and the Askey-Wilson polynomials. Methods and Appl. Anal. 2, 369-398 (1995)
    • (1995) Methods and Appl. Anal. , vol.2 , pp. 369-398
    • Spiridonov, V.1    Zhedanov, A.2
  • 18
    • 0031583014 scopus 로고    scopus 로고
    • Discrete-time Volterra chain and classical orthogonal polynomials
    • 18. Spiridonov, V. and Zhedanov, A., Discrete-time Volterra chain and classical orthogonal polynomials. J. Phys. A: Math. & Gen. 30, 8727-8737 (1997)
    • (1997) J. Phys. A: Math. & Gen. , vol.30 , pp. 8727-8737
    • Spiridonov, V.1    Zhedanov, A.2
  • 19
    • 0004073954 scopus 로고
    • Providence, RI: Am. Math. Soc., second edition
    • 19. SzegoÖ, G.: Orthogonal Polynomials. Providence, RI: Am. Math. Soc., 1959 (second edition)
    • (1959) Orthogonal Polynomials
    • Szegoö, G.1
  • 23
    • 0000102490 scopus 로고
    • Orthogonal functions from Gram determinants
    • 23. Wilson, J.A.: Orthogonal functions from Gram determinants. SIAM J. Math. Anal. 22, 1147-1155 (1991)
    • (1991) SIAM J. Math. Anal. , vol.22 , pp. 1147-1155
    • Wilson, J.A.1
  • 24
    • 0033474021 scopus 로고    scopus 로고
    • Biorthogonal rational functions and generalized eigenvalue problem
    • to be published
    • 24. Zhedanov, A.: Biorthogonal rational functions and generalized eigenvalue problem. J. Approx. Theory, to be published
    • J. Approx. Theory
    • Zhedanov, A.1
  • 25
    • 0033439813 scopus 로고    scopus 로고
    • Hypergeometric biorthogonal rational functions
    • in Russian
    • 25. Zhedanov, A. and Spiridonov, V.: Hypergeometric biorthogonal rational functions. Uspekhi Mat. Nauk (Russian Math. Surveys) 54 No. 2, 173-174 (1999) (in Russian)
    • (1999) Uspekhi Mat. Nauk (Russian Math. Surveys) , vol.54 , Issue.2 , pp. 173-174
    • Zhedanov, A.1    Spiridonov, V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.