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Volumn 13, Issue 1-3, 2007, Pages 285-310

Elliptic grids, rational functions, and the Padé interpolation

Author keywords

Divided difference operators; Elliptic functions; Pad interpolation; Poncele porism

Indexed keywords


EID: 33845794288     PISSN: 13824090     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11139-006-0253-1     Document Type: Conference Paper
Times cited : (15)

References (35)
  • 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, 319 (1985)
    • (1985) Mem. Amer. Math. Soc. , vol.54 , pp. 319
    • Askey, R.1    Wilson, J.2
  • 5
    • 84968468972 scopus 로고
    • A fast algorithm for rational interpolation via orthogonal polynomials
    • Egecioglu, O., Koc, C.K.: A fast algorithm for rational interpolation via orthogonal polynomials. Math. Comp. 53, 249-264 (1989)
    • (1989) Math. Comp. , vol.53 , pp. 249-264
    • Egecioglu, O.1    Koc, C.K.2
  • 6
    • 0001432807 scopus 로고    scopus 로고
    • Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions
    • Birkhäuser, Boston, MA
    • Frenkel, I.B., Turaev, V.G.: Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions. The Arnold-Gelfand Mathematical Seminars, pp. 171-204. Birkhäuser, Boston, MA (1997)
    • (1997) The Arnold-Gelfand Mathematical Seminars , pp. 171-204
    • Frenkel, I.B.1    Turaev, V.G.2
  • 7
    • 33746682231 scopus 로고    scopus 로고
    • Basic hypergeometric series
    • Cambridge Univ. Press, Cambridge
    • Gasper, G., Rahman, M.: Basic hypergeometric series. Encyclopedia of Math. Appl., vol. 96. Cambridge Univ. Press, Cambridge (2004)
    • (2004) Encyclopedia of Math. Appl. , vol.96
    • Gasper, G.1    Rahman, M.2
  • 9
    • 0002320840 scopus 로고
    • On a Cayley's explicit solution to Poncelet's porism
    • Griffiths, P., Harris, J.: On a Cayley's explicit solution to Poncelet's porism. Enseign. Math. 24(2), 31-40 (1978)
    • (1978) Enseign. Math. , vol.24 , Issue.2 , pp. 31-40
    • Griffiths, P.1    Harris, J.2
  • 10
    • 0141820548 scopus 로고
    • Generalized orthogonality and continued fractions
    • Ismail, M.E.H., Masson, D.: 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.2
  • 11
    • 8144224911 scopus 로고
    • Rational interpolation to exp(-x) with application to certain stiff systems
    • Iserles, A.: Rational interpolation to exp(-x) with application to certain stiff systems. SIAM J. Numer. Anal. 18, 1-12 (1981)
    • (1981) SIAM J. Numer. Anal. , vol.18 , pp. 1-12
    • Iserles, A.1
  • 13
    • 0004548025 scopus 로고
    • Associated Askey-Wilson polynomials as Laguerre-Hahn orthogonal polynomials
    • Orthogonal Polynomials and Their Applications. Proc. Internat. Symposium (Segovia, Spain, September 22-27, 1986)
    • Magnus, A.: Associated Askey-Wilson polynomials as Laguerre-Hahn orthogonal polynomials. Orthogonal Polynomials and Their Applications. Proc. Internat. Symposium (Segovia, Spain, September 22-27, 1986). Lect. Notes Math. 1329, 261-278 (1988)
    • (1988) Lect. Notes Math. , vol.1329 , pp. 261-278
    • Magnus, A.1
  • 14
    • 0000479720 scopus 로고
    • Special nonuniform lattice (snul) orthogonal polynomials on discrete dense sets of points
    • Magnus, A.: Special nonuniform 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
  • 15
    • 0040570582 scopus 로고
    • On the solubility of the Cauchy interpolation problem
    • Lancaster. Academic Press, London
    • Meinguet, J.: On the solubility of the Cauchy interpolation problem. Approximation Theory (Proc. Sympos., Lancaster, 1969) pp. 137-163. Academic Press, London (1970)
    • (1969) Approximation Theory Proc. Sympos. , pp. 137-163
    • Meinguet, J.1
  • 17
    • 0000946162 scopus 로고
    • An integral representation of a 10.9 and continuous biorthogonal 10.9 rational functions
    • Rahman, M.: An integral representation of a 10.9 and continuous biorthogonal 10.9 rational functions. Canad. J. Math. 38, 605-618 (1986)
    • (1986) Canad. J. Math. , vol.38 , pp. 605-618
    • Rahman, M.1
  • 18
    • 0000815807 scopus 로고
    • Classical biorthogonal rational functions
    • Methods of Approximation Theory in Complex Analysis and Mathematical Physics IV, Springer-Verlag, Berlin
    • Rahman, M., Suslov, S.: Classical biorthogonal rational functions. Methods of Approximation Theory in Complex Analysis and Mathematical Physics IV, Lect. Notes Math., vol. 1550, pp. 131-146. Springer-Verlag, Berlin (1993)
    • (1993) Lect. Notes Math. , vol.1550 , pp. 131-146
    • Rahman, M.1    Suslov, S.2
  • 20
    • 33750306780 scopus 로고    scopus 로고
    • BCn-symmetric abelian functions
    • (to appear)
    • Rains, E.M.: BCn-symmetric abelian functions. Duke Math. J. (to appear)
    • Duke Math. J.
    • Rains, E.M.1
  • 21
    • 33845728851 scopus 로고    scopus 로고
    • An elemenatry approach to 6 j-symbols (classical, quantum, rational, trigonometric and elliptic)
    • 2007
    • Rosengren, H.: An elemenatry approach to 6 j-symbols (classical, quantum, rational, trigonometric and elliptic). Ramanujan J. 13(1/2/3), 131-166 (2007)
    • Ramanujan J. , vol.13 , Issue.1-3 , pp. 131-166
    • Rosengren, H.1
  • 23
    • 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
  • 25
    • 0034349855 scopus 로고    scopus 로고
    • Spectral transformation chains and some new biorthogonal rational functions
    • Spiridonov, V.P., Zhedanov, A.S.: Spectral transformation chains and some new biorthogonal rational functions. Commun. Math. Phys. 210, 49-83 (2000)
    • (2000) Commun. Math. Phys. , vol.210 , pp. 49-83
    • Spiridonov, V.P.1    Zhedanov, A.S.2
  • 26
    • 0242575584 scopus 로고    scopus 로고
    • Generalized eigenvalue problem and a new family of rational functions biorthogonal on elliptic grids
    • Kluwer, Dordrecht
    • Spiridonov, V.P., Zhedanov, A.S.: Generalized eigenvalue problem and a new family of rational functions biorthogonal on elliptic grids. Special Functions 2000, pp. 365-388. Kluwer, Dordrecht (2001)
    • (2001) Special Functions 2000 , pp. 365-388
    • Spiridonov, V.P.1    Zhedanov, A.S.2
  • 27
    • 23944487929 scopus 로고    scopus 로고
    • To the theory of biorthogonal rational functions
    • Spiridonov, V.P., Zhedanov, A.S.: To the theory of biorthogonal rational functions. RIMS Kokyuroku 1302, 172-192 (2003)
    • (2003) RIMS Kokyuroku , vol.1302 , pp. 172-192
    • Spiridonov, V.P.1    Zhedanov, A.S.2
  • 28
    • 0009029770 scopus 로고
    • Existence and uniqueness of rational interpolants with free and prescribed poles
    • Approximation Theory (Tampa, FL, 1985-1986), Springer, Berlin
    • Stahl, H.: Existence and uniqueness of rational interpolants with free and prescribed poles. Approximation Theory (Tampa, FL, 1985-1986), Lect. Notes Math., vol. 1287, pp. 180-208. Springer, Berlin (1987)
    • (1987) Lect. Notes Math. , vol.1287 , pp. 180-208
    • Stahl, H.1
  • 29
    • 0002859048 scopus 로고
    • Integrable systems with discrete time and difference operators
    • (Russian)
    • Veselov, A.P.: Integrable systems with discrete time and difference operators. Functional Analysis and its Applications 22, 1-13 (1988) (Russian)
    • (1988) Functional Analysis and Its Applications , vol.22 , pp. 1-13
    • Veselov, A.P.1
  • 31
    • 0000102490 scopus 로고
    • Orthogonal functions from Gram determinants
    • 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
  • 32
    • 0033474021 scopus 로고    scopus 로고
    • Biorthogonal rational functions and the generalized eigenvalue problem
    • Zhedanov, A.: Biorthogonal rational functions and the generalized eigenvalue problem. J. Approx. Theory 101, 303-329 (1999)
    • (1999) J. Approx. Theory , vol.101 , pp. 303-329
    • Zhedanov, A.1
  • 33
    • 33845732005 scopus 로고    scopus 로고
    • Explicit multipoint rational interpolation Padé table for exponential and power functions
    • CRM. Montréal, May 26-31
    • Zhedanov, A.: Explicit multipoint rational interpolation Padé table for exponential and power functions. Workshop on Group Theory and Numerical Analysis, CRM. Montréal, May 26-31 (2003)
    • (2003) Workshop on Group Theory and Numerical Analysis
    • Zhedanov, A.1
  • 34
    • 4444338902 scopus 로고    scopus 로고
    • Biorthogonality of the Lagrange interpolants
    • Zhedanov, A.: Biorthogonality of the Lagrange interpolants. J. Comp. Appl. Math. 172, 1-6 (2004)
    • (2004) J. Comp. Appl. Math. , vol.172 , pp. 1-6
    • Zhedanov, A.1
  • 35
    • 57049151983 scopus 로고    scopus 로고
    • Padé interpolation table and biorthogonal rational functions
    • Kyoto, November 8-11 to be published
    • Zhedanov, A.: Padé interpolation table and biorthogonal rational functions. In: Proceedings of RIMS Workshop on Elliptic Integrable Systems. Kyoto, November 8-11 (2004) to be published
    • (2004) Proceedings of RIMS Workshop on Elliptic Integrable Systems
    • Zhedanov, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.